16  Hypothesis Testing and Confidence Intervals in Two Populations

With confidence intervals and hypothesis tests we began to make inferences regarding populations by quantifying our levels of uncertainty. Quantifying uncertainty sits at the core of inferential statistics, and through this we are able to effectively draw conclusions and learn about populations. With that said, the procedures discussed so far have focused on individual parameters from individual populations. While there are many scientific questions relating to a single parameter from a single population, it is perhaps more common to consider the comparison between two populations.¹ To answer questions relating to the comparison of multiple populations, we must extend the ideas of hypothesis testing and confidence intervals to the setting where we have samples from two (or more) populations.

16.1 Two Populations Rather than One

In the one population setting we supposed that we observed \(X_1,\dots,X_n\) as an independent and identically distributed sample from some population. We then considered parameters of this population² and addressed questions relating to these parameters. In the two population setting, we introduce a second independent and identically distributed sample, \(Y_1,\dots,Y_m\), from a second population. The distribution for the \(Y\)s may or may not be the same distribution as the distribution for the \(X\)s. Moreover, the distribution of \(X\) and of \(Y\) may be independent of one another, or they may be related to one another. We will take \(F_X\) and \(F_Y\) to represent the distribution of \(X\) and the distribution of \(Y\), respectively, and we will use the same notational conventions for the parameters of these distributions. So, for instance, we may take \(\mu_X\) and \(\mu_Y\) to represent the population means, or \(\sigma_X^2\) and \(\sigma_Y^2\) to represent the population variances. The size of the samples we draw may be equal, or not. We assume that there are \(n\) observations taken from \(F_X\) and there are \(m\) observations taken from \(F_Y\). Each of these samples could be used for individual hypothesis testing or estimation, using the procedures that we have previously seen.

We will typically be concerned with the same parameters and estimators we have been considering previously. For instance, it is common to consider the population means. To this end we have \(\mu_X\), which can be estimated by \(\overline{X}\), and we have \(\mu_Y\), which can be estimated by \(\overline{Y}\). Even if \(\mu_X = \mu_Y\) in practice, it is unlikely that we will observe \(\overline{X} = \overline{Y}\), exactly. This may lead us to consider whether we can perform a hypothesis test that asks whether, based on the observed information, the two populations have exactly the same mean.

To do this, we want to test \(H_0: \mu_X = \mu_Y\) versus the alternative, \(H_A: \mu_X \neq \mu_Y\). In order to determine how to test this hypothesis, it is helpful to re-express it as a single parameter. Notice that if \(\mu_X = \mu_Y\), then \(\mu_X - \mu_Y = 0\). We can rewrite the previous hypotheses as \(H_0: \mu_X - \mu_Y = 0\) and \(H_A: \mu_X - \mu_Y \neq 0\). If we define a new parameter, \(\Delta = \mu_X - \mu_Y\), such that \(\Delta\) represents the difference in mean values for the two distributions,³ then we can state our hypothesis test as \(H_0: \Delta = 0\) versus \(H_A: \Delta \neq 0\).

This test is no different from any of the tests we have seen before. If we can work out an estimator for \(\Delta\), and work out the null distribution for this estimator, we can use the procedures outlined for null hypothesis significance testing to assess how much evidence exists against the hypothesis that the means are equal. Similarly, if we are able to work out an estimator for \(\Delta\), and we can identify the sampling distribution of this estimator, then we can form confidence intervals for \(\Delta\), allowing both point and interval estimation to proceed for the difference in population means.

In order to estimate \(\Delta\), it is helpful to consider that \(\Delta = \mu_X - \mu_Y\). We know that \(\overline{X}\) is an effective estimator for \(\mu_X\) and that \(\overline{Y}\) is an effective estimator for \(\mu_Y\). Taken together, it is reasonable to suggest that an estimator for \(\Delta\) is given by \[\widehat{\Delta} = \overline{X} - \overline{Y}.\] Since both \(\overline{X}\) and \(\overline{Y}\) are unbiased for \(\mu_X\) and \(\mu_Y\), then \(\widehat{\Delta}\) will also be unbiased for \(\Delta\). If we are able to assess the null and sampling distributions of \(\widehat{\Delta}\), we can leverage the same procedures for confidence intervals and hypothesis tests we have already discussed. Determining these distributions depends on the assumptions made regarding the distributions \(F_X\) and \(F_Y\), as well as the relationship between them.

Note that the same general approach could have been used to test hypotheses beyond the equality of the population means. For instance, suppose we wanted to know whether the mean of \(X\) was \(10\) units larger than the mean of \(Y\). This corresponds to \(\mu_X = \mu_Y + 10\), or \(\mu_X - \mu_Y = 10\), and so we can test it using \(H_0: \Delta = 10\) versus the alternative \(H_0: \Delta \neq 10\). Alternatively, what if we had hypothesized that \(\mu_X\) was really half as large as \(\mu_Y\)? In this case, we get that \(2\mu_X = \mu_Y\), or \(2\mu_X - \mu_Y = 0\). Now, if we introduce \(\Delta_{2} = 2\mu_X - \mu_Y\) then we can test \(H_0: \Delta_2 = 0\) versus \(H_A: \Delta_2 \neq 0\). To estimate \(\Delta_2\), we can note that \(2\mu_X\) is estimated well by \(2\overline{X}\), and so \[\widehat{\Delta}_2 = 2\overline{X} - \overline{Y},\] is a reasonable estimator.⁴

Beyond testing additional hypotheses related to the mean difference, we can also test alternative parameters in the distribution using a similar approach. Suppose we have two separate binomial distributions. Here we may have \(p_X\) and \(p_Y\) as the relevant proportions, and we may be interested in testing whether \(p_X = p_Y\) or not. To do so, we can use the exact same procedure, taking \(\Delta = p_X - p_Y\), and testing \(H_0: \Delta = 0\) versus \(H_A: \Delta \neq 0\).⁵ Because \(\widehat{p} = \overline{X}\), we can use the exact same estimator, \(\widehat{\Delta}\), and continue in the same process outlined above. Alternatively, we may consider the variances of the population. By framing \(\sigma_X^2 = \sigma_Y^2\), we can follow a similar procedure, either taking the difference \(\Delta = \sigma_X^2 - \sigma_Y^2\), or, more commonly, the ratio, \(\rho = \dfrac{\sigma_X^2}{\sigma_Y^2}\), and then testing hypothesis such as \(H_0: \Delta = 0\) or \(H_0: \rho = 1\), versus the alternatives \(H_A: \Delta \neq 0\) or \(H_A: \rho \neq 1\).

The key idea when dealing with two samples from two populations is to frame the question in terms of a parameter of the joint distribution. Then, estimation (point and interval), and hypothesis testing can proceed on the basis of the single parameter that has been identified. At this point, it is a matter of working out the sampling distribution, and implementing the same procedures explored in the one sample case. The difficulty lies in determining the sampling and null distributions of these estimators.

16.2 Hypothesis Tests and Confidence Intervals for Mean Differences in Independent Populations

In order to determine the sampling and null distribution when dealing with two samples of data, a key assumption that needs to be clarified is whether or not the populations are independent of one another. If we know that \(X \perp Y\), then it is typically more straightforward to derive the sampling and null distributions. Consider, specifically, \(\Delta = \mu_X - \mu_Y\). As discussed, we can estimate \(\Delta\) using \(\widehat{\Delta} = \overline{X} - \overline{Y}\). We have seen that \[\overline{X} \sim N(\mu_X, \sigma_X^2) \quad\text{ and }\quad \overline{Y} \sim N(\mu_Y, \sigma_Y^2),\] where these are the exact distributions if the populations are normal, and these hold approximately in large samples otherwise. Note that, regardless of the dependence or independence of \(X\) and \(Y\), it will always be the case that \[E[\widehat{\Delta}] = E[\overline{X}] - E[\overline{Y}] = \mu_X - \mu_Y = \Delta.\] That is, \(\widehat{\Delta}\) is unbiased for \(\Delta\). If we are willing to assume that \(X \perp Y\), then \[\text{var}(\widehat{\Delta}) = \text{var}(\overline{X}) + \text{var}(\overline{Y}) = \frac{\sigma_X^2}{n} + \frac{\sigma_Y^2}{m}.\]

If the two samples we take are independent of one another, then we can conclude that \[\widehat{\Delta} \sim N(\Delta, \frac{\sigma_X^2}{n} + \frac{\sigma_Y^2}{m}).\] This result immediately allows for the calculation of confidence intervals, using the normal based confidence intervals previously investigated, whenever the variance terms, \(\sigma_X^2\) and \(\sigma_Y^2\) are known. If these variances are unknown, then the variance can be estimated using the individual sample variances, \(S_X^2\) and \(S_Y^2\). Replacing \(\sigma_X^2\) and \(\sigma_Y^2\) with these results in an underlying \(t\) distribution, with \(\nu\) degrees of freedom, where \[\nu = \frac{\left(\frac{S_X^2}{n} + \frac{S_Y^2}{m}\right)^2}{\frac{(S_X^2/n)^2}{n-1} + \frac{(S_Y^2/m)^2}{m-1}}.\] Note that this is typically a fairly complicated expression, and so instead we will often take \(\nu = \min\{n-1,m-1\}\). Then, confidence intervals for \(\widehat{\Delta}\) can be formed using the \(t\) distribution, following the same procedure as our other \(t\) distribution confidence intervals.

Confidence Intervals for Differences of Means in Independent Populations

If we wish to estimate the difference of two population means, \(\mu_X - \mu_Y\), from populations that are independent of one another, then we can form confidence \(Z\)- or \(t\)-based confidence intervals, depending on whether the variances are known or not.

1. If \(\sigma_X^2\) and \(\sigma_Y^2\) are known, then \[\overline{X} - \overline{Y} \pm Z_{\alpha/2}\sqrt{\frac{\sigma_X^2}{n} + \frac{\sigma_Y^2}{m}}.\]
2. If \(\sigma_X^2\) and \(\sigma_Y^2\) are unknown, then \[\overline{X} - \overline{Y} \pm t_{\nu, \alpha/2}\sqrt{\frac{S_X^2}{n} + \frac{S_Y^2}{m}} \quad\text{where}\quad \nu = \frac{\left(\frac{S_X^2}{n} + \frac{S_Y^2}{m}\right)^2}{\frac{(S_X^2/n)^2}{n-1} + \frac{(S_Y^2/m)^2}{m-1}}.\] Here, \(\nu\) is often taken to be \(\min\{n-1, m-1\}\) instead.

Under the null hypothesis that \(\Delta = \Delta_0\), for some constant \(\Delta_0\), we can transform the sampling distribution to the null distribution by noting that the mean will be \(\Delta_0\), and the variance will remain unchanged. Then, depending on whether the variances are assumed to be known, or not, we can use a \(Z\)-test or a \(t\)-test for hypothesis testing.

Hypothesis Tests for Differences of Means in Independent Populations

If we have data selected from two, independent populations (denoted \(X_1,\dots,X_n\) and \(Y_1,\dots,Y_m\)), and we wish to test hypotheses relating to the relationship in population means, we can use a \(Z\)- or \(t\)-test, based on our knowledge of the population variances.

1. If \(\sigma_X^2\) and \(\sigma_Y^2\) are known, then \[T = \frac{\overline{X} - \overline{Y} - \Delta_0}{\sqrt{\frac{\sigma_X^2}{n} + \frac{\sigma_Y^2}{m}}} \stackrel{H_0}{\sim} N(0, 1).\] Assuming that we observe \(T=t\),
   1. If \(H_0: \Delta = \Delta_0\) versus \(H_A: \Delta \neq \Delta_0\) then the \(p\)-value is \(2\Phi(-|t|)\). The critical value is \(Z_{1-\alpha/2}\).
   2. If \(H_0: \Delta \geq \Delta_0\) versus \(H_A: \Delta < \Delta_0\) then the \(p\)-value is \(\Phi(t)\). The corresponding critical value is \(Z_{\alpha}\).
   3. If \(H_0: \Delta \leq \Delta_0\) versus \(H_A: \Delta > \Delta_0\) then the \(p\)-value is \(1 - \Phi(t)\). The corresponding critical value is \(Z_{1-\alpha}\).
2. If the variances are unknown, then we take \[T = \frac{\overline{X} - \overline{Y} - \Delta_0}{\sqrt{\frac{S_X^2}{n} + \frac{S_Y^2}{m}}} \stackrel{H_0}{\sim} t_\nu,\quad\text{with}\quad\nu = \frac{\left(\frac{S_X^2}{n} + \frac{S_Y^2}{m}\right)^2}{\frac{(S_X^2/n)^2}{n-1} + \frac{(S_Y^2/m)^2}{m-1}}.\] Taking \(F(t)\) to be the cumulative distribution function for the \(t_\nu\) distribution, and assuming we observe \(T=t\),
   1. If \(H_0: \Delta = \Delta_0\) versus \(H_A: \Delta \neq \Delta_0\) then the \(p\)-value is \(2F(-|t|)\). The critical value is \(t_{\nu, 1-\alpha/2}\).
   2. If \(H_0: \Delta \geq \Delta_0\) versus \(H_A: \Delta < \Delta_0\) then the \(p\)-value is \(F(t)\). The corresponding critical value is \(t_{\nu, \alpha}\).
   3. If \(H_0: \Delta \leq \Delta_0\) versus \(H_A: \Delta > \Delta_0\) then the \(p\)-value is \(1 - F(t)\). The corresponding critical value is \(t_{\nu, 1-\alpha}\).

16.2.1 Pooled Variance Estimation

Sometimes, even when \(\sigma_X^2\) and \(\sigma_Y^2\) are unknown, it is reasonable to assume that the variances of the two populations will be equal. That is, we may have good reason to suspect that \(\sigma_X^2 = \sigma_Y^2\), even if we do not know the value of \(\sigma_X^2\).⁶ In these settings, instead of taking two separate variances, we ultimately have a single parameter, \(\sigma^2\). When this happens, we can revisit the sampling distribution, noting that \[\overline{X} - \overline{Y} \sim N\left(\Delta, \sigma^2\left[\frac{1}{n}+\frac{1}{m}\right]\right).\] If \(\sigma^2\) is known, then the previously discussed sampling and null distributions are valid, taking \[\frac{\sigma_X^2}{n} + \frac{\sigma_Y^2}{m} = \sigma^2\left(\frac{1}{n} + \frac{1}{m}\right).\]

If the variance is unknown, it still needs to be estimated using the data. This can be done using the pooled variance estimator, \(S_p^2\). Namely, \[S_p^2 = \frac{(n-1)S_X^2 + (m-1)S_Y^2}{n+m-2}.\] Leveraging this pooled variance estimator gives \[\frac{\overline{X} - \overline{Y} - \Delta}{S_p\sqrt{\frac{1}{n} + \frac{1}{m}}} \sim t_{n+m-2},\] and the equivalent null distribution when \(\Delta\) is replaced by \(\Delta_0\). Note that here there are \(n+m-2\) degrees of freedom. Otherwise, the same procedures – either using the \(Z\)-based or \(t\)-based intervals or tests – can proceed with the pooled variance in place of the independent variances.

The pooled variance estimator represents an anti-conservative approach to quantifying uncertainty. That is, if the same analysis is done with the pooled variance and with the unpooled variances, you should expect narrower confidence intervals and smaller \(p\)-values if the pooled variance is used. This can be an effective way of making complete use of prior knowledge, when the variances of the populations are actually equal. However, in the event that the variances are not actually equal, using the pooled variances will lead to erroneous conclusions. For this reason, you should rely on subject-matter guidance to determine whether equal variances should be assumed. If there is a strong scientific basis for the equality of the variances, and the data do not seem to dramatically contradict this assumption, then using pooled variances may be reasonable. Otherwise, you should estimate the variances separately.

16.2.2 Confidence Intervals and Hypothesis Tests for Multiple Proportions

The previous discussions centered around testing population means. Implicitly, this investigated populations that are continuous, where the mean is the primary measure of interest. The same techniques apply equally well to considering two population proportions. Namely, if \(X \sim \text{Bin}(n, p_X)\), and \(Y \sim \text{Bin}(m, p_Y)\), it may be of interest to us to determine the relationship between \(p_X\) and \(p_Y\). We may wish to proceed either with the estimation (point and interval) of the difference between \(p_X\) and \(p_Y\), or else to test hypotheses regarding the relationship of \(p_X\) and \(p_Y\). Recall that in the case of a single proportion we made use of the fact that, for large samples, the sample proportion will be approximately normally distributed. The same general technique applies in the case of two populations.

Since both \(\widehat{p}_X\) and \(\widehat{p}_Y\) are approximately normally distributed, their difference will also be approximately normally distributed. Supposing that we are willing to assume that \(X\perp Y\), then \[\widehat{p}_X - \widehat{p}_Y \sim N\left(p_X - p_Y, \frac{p_X(1-p_X)}{n} + \frac{p_Y(1-p_Y)}{m}\right).\] This sampling distribution allows for the construction of approximate confidence intervals for the difference in proportions.

Confidence Intervals for Differences of Proportions in Independent Populations

To estimate the difference of two population proportions, \(p_X - p_Y\), from populations that are independent of one another, we can form confidence \(Z\)-based confidence intervals. Supposing that \(n\) and \(m\) are both sufficiently large, take \[\widehat{p}_X - \widehat{p}_Y \pm Z_{\alpha/2}\sqrt{\frac{\widehat{p}_X(1-\widehat{p}_X)}{n} + \frac{\widehat{p}_Y(1-\widehat{p}_Y)}{m}}.\]

If there is a desire to ensure that the computed interval is conservative, then \(\widehat{p}_X\) and \(\widehat{p}_Y\) can both be replaced by \(0.5\). This will maximize the standard error, and will ensure coverage of the interval even if the estimated proportion is off in the current sample.

The same approach can be extended to test hypotheses relating to the population differences. If we consider the hypothesis \(H_0: p_X - p_Y = 0\), then assuming the null hypothesis holds we know that \(p_X = p_Y = p\), for some value \(p\). If this is the case then the variance of \(\widehat{p}_X - \widehat{p}_Y\) can be expressed as \[\text{var}(\widehat{p}_X - \widehat{p}_Y) = p(1-p)\left(\frac{1}{n} + \frac{1}{m}\right).\] This variance is maximized by taking \(p = 0.5\), and so we can ensure conservative hypothesis tests of the hypothesis \(H_0: p_X - p_Y = 0\) (or the one-sided alternatives). On the other hand, suppose that the null hypothesis was given by \(p_X - p_Y = c\), for \(c \neq 0\). Then, \(p_X = p + c\) and \(p_Y = p\), for some proportion \(p\). In this setting, \[\text{var}(\widehat{p}_X - \widehat{p}_Y) = \frac{(p+c)(1-(p+c))}{n} + \frac{p(1-p)}{m}.\] This does not simplify in the way that the variance expression simplifies under the null hypothesis of equality. Further, this expression is not easily maximized over \(p\). Without careful choice of \(p\) this approximation tends to perform rather poorly. As a result, if we wish to test \(H_0: p_X - p_Y = c\), for any \(c \neq 0\), then we require alternative procedures, not relying on the normal approximation.

Hypothesis Tests for Equality of Proportions in Two Independent Populations

To test \(H_0: p_X - p_Y = 0\) versus the alternative \(H_A: p_X - p_Y \neq 0\), using data from two independent populations, with success proportions \(p_X\) and \(p_Y\) respectively, we can use a \(Z\)-test based on \[T = \frac{\widehat{p}_X - \widehat{p}_Y}{0.5\sqrt{\frac{1}{n} + \frac{1}{m}}} \stackrel{H_0}{\sim} N(0,1).\] Then, the two-tailed \(p\)-value can be computed as \(2\times\Phi(-|t|)\), when \(T=t\).

• To test \(H_0: p_X - p_Y \geq 0\) versus the alternative \(H_A: p_X - p_Y < 0\), the \(p\)-value will be given by \(\Phi(t)\).
• To test \(H_0: p_X - p_Y \leq 0\) versus the alternative \(H_A: p_X - p_Y > 0\), the \(p\)-value will be given by \(1 - \Phi(t)\).

16.3 The Analysis of Paired Data

When the populations are independent from one another, regardless of whether a common variance is assumed or not, the two-population problem can be transformed into a question regarding a single parameter by adequately adjusting the sampling and the null distributions. Ultimately, this results in the same \(Z\)- and \(t\)-based procedures introduced previously. It will often be the case, however, that we cannot assume independence between the populations. If we cannot assume independence between the two populations, there will not be a single method of proceeding with investigating mean differences. Instead, our results will depend on the manner in which the populations are dependent. While many different forms of dependence may be of interest, a common assumption is that the populations are paired. By paired we mean that \(X_i\) and \(Y_i\) are observations that are naturally connected to one another, for instance, by being measurements of different quantities on the same unit, or measurements of the same unit overtime, or similar. When data are paired, it will always be the case that the samples are of the same size, taking \(n=m\).

Definition 16.1 (Paired Data) Paired data refer to observations in a dataset that are linked to one another through some underlying, natural connection. Data may be paired because they are taken on the same unit, or because the observations are connected in another meaningful way. In paired data, there is an obvious and meaningful one-to-one correspondence between measurements of one variable and another.

Suppose, for instance, that we measure the same trait at two different points in time, for all the same units. Then \(X_1,\dots,X_n\) correspond to the first measurements that are taken, and \(Y_1,\dots,Y_n\) correspond to the second. Here, \(X_1\) and \(Y_1\) are naturally paired since they are the same unit observed at two points in time. We expect that \(X_1\) and \(Y_1\) will be related to one another, though, not exactly the same. The same can be said for \(X_2\) and \(Y_2\), and more generally for \(X_i\) and \(Y_i\). When data are paired they are not independent.

Suppose that, with paired data, we are concerned with hypotheses regarding mean differences, considering for instance \(H_0: \mu_X - \mu_Y = 0\). In independent samples we considered the difference of sample means as an estimator, \(\overline{X} - \overline{Y}\), where the samples of \(X\) and \(Y\) could have been of possibly different sizes. If we consider the same quantities when data are paired, we can rewrite the expression as follows: \[\begin{align*} \overline{X} - \overline{Y} &= \frac{1}{n}\sum_{i=1}^n X_i - \frac{1}{n}\sum_{i=1}^n Y_i \\ &= \frac{1}{n}\sum_{i=1}^n (X_i - Y_i) \\ &= \frac{1}{n}\sum_{i=1}^n D_i. \end{align*}\] Here, \(D_i = X_i - Y_i\) is the difference between \(X\) and \(Y\) within each pair. In other words, when data are paired, we can first consider the differences between observations, giving a set of \(n\) observations, \(D_1, \dots, D_n\). Then, using this single sample, we can construct confidence intervals or perform hypothesis tests.

Once the sample of differences is formed, the problem of interval estimation or hypothesis testing is no different from the one sample procedures outlined. The sampling distribution of \(\overline{D}\) is exactly normal if both \(X_i\) and \(Y_i\) are exactly normal, and it will be approximately normal using the Central Limit Theorem if \(n\) is sufficiently large. The expected value, \(E[\overline{D}] = \mu_X - \mu_Y\), according to the exact same logic applied for the independent case. The only slight difficulty is with the variance, where notably \[\text{var}(\overline{D}) = \frac{\sigma_X^2 + \sigma_Y^2 - 2\sigma_{XY}}{n}.\] Here \(\sigma_{XY}\) is the covariance between \(X\) and \(Y\) (Definition 7.4).⁷ Typically, for paired data, \(\sigma_{XY} > 0\) and so the variance will be smaller than when it is assumed that \(X\) and \(Y\) are independent of one another. Because of this, making the assumption that the data are paired is an anti-conservative assumption. There needs to be good reason to suppose that \(X\) and \(Y\) really are paired, and that they should be analyzed in this manner, as otherwise the \(p\)-values may be artificially deflated.

Confidence Intervals for Differences of Means in Paired Populations

To estimate the difference of two population means, \(\mu_X - \mu_Y\), from populations that are paired with one another, we can form confidence \(Z\)- or \(t\)-based confidence intervals, depending on whether the variances are known or not. First, we find the paired differences, \(D_i = X_i - Y_i\), and then consider the sample \(D_1, \dots, D_n\) as a single sample. The variance of \(D_i\) is given by \[\text{var}(D_i) = \sigma_D^2 = \sigma_X^2 + \sigma_Y^2 - 2\sigma_{XY}.\]

1. If \(\sigma_D^2\) is known, take \[\overline{D} \pm Z_{\alpha/2}\frac{\sigma_D}{\sqrt{n}}.\]
2. If \(\sigma_D^2\) is unknown, take \[\overline{D} \pm t_{n-1, \alpha/2}\frac{S_D}{\sqrt{n}}.\]

Hypothesis Tests for Differences of Means in Paired Populations

If we have data selected from two, paired populations (denoted \(X_1,\dots,X_n\) and \(Y_1,\dots,Y_m\)), to test hypotheses relating to the relationship in population means, we can use a \(Z\)- or \(t\)-test, based on our knowledge of the population variances. First, we find the paired differences, \(D_i = X_i - Y_i\), and then consider the sample \(D_1, \dots, D_n\) as a single sample. The variance of \(D_i\) is given by \[\text{var}(D_i) = \sigma_D^2 = \sigma_X^2 + \sigma^2 - 2\sigma_{XY}.\]

1. If \(\sigma_D^2\) is known, then we take \[Z = \frac{\overline{D} - D_0}{\sigma_D/\sqrt{n}} \stackrel{H_0}{\sim} N(0, 1).\] If we observe \(T=t\),
   1. If \(H_0: D = D_0\) versus \(H_A: D \neq D_0\) then the \(p\)-value is \(2\Phi(-|t|)\). The critical value is \(Z_{1-\alpha/2}\).
   2. If \(H_0: D \geq D_0\) versus \(H_A: D < D_0\) then the \(p\)-value is \(\Phi(t)\). The corresponding critical value is \(Z_{\alpha}\).
   3. If \(H_0: D \leq D_0\) versus \(H_A: D > D_0\) then the \(p\)-value is \(1 - \Phi(t)\). The corresponding critical value is \(Z_{1-\alpha}\).
2. If \(\sigma_D^2\) is unknown, then we take \[T = \frac{\overline{D} - D_0}{S_D/\sqrt{n}} \stackrel{H_0}{\sim} t_{n-1}.\] Taking \(F(t)\) to be the cumulative distribution function for the \(t_{n-1}\) distribution, and assuming we observe \(T=t\),
   1. If \(H_0: D = D_0\) versus \(H_A: D \neq D_0\) then the \(p\)-value is \(2F(-|t|)\). The critical value is \(t_{\nu, 1-\alpha/2}\).
   2. If \(H_0: D \geq D_0\) versus \(H_A: D < D_0\) then the \(p\)-value is \(F(t)\). The corresponding critical value is \(t_{\nu, \alpha}\).
   3. If \(H_0: D \leq D_0\) versus \(H_A: D > D_0\) then the \(p\)-value is \(1 - F(t)\). The corresponding critical value is \(t_{\nu, 1-\alpha}\).

Self-Assessment

Note: the following questions are still experimental. Please contact me if you have any issues with these components. This can be if there are incorrect answers, or if there are any technical concerns. Each question currently has an ID with it, randomized for each version. If you have issues, reporting the specific ID will allow for easier checking!

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Self Assessment 16.1

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 448 individuals on the first diet (labeled \(X\)). Further, they take a sample of 66 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 101.82\) and \(\overline{Y} = 100.81\). Moreover, they know that \(\sigma_X = 7.8\) and \(\sigma_Y = 9.94\).

The interest of the study is in testing whether individuals on the first diet have lower average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0075755065

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 79 individuals on the first diet (labeled \(X\)). Further, they take a sample of 167 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 175.65\) and \(\overline{Y} = 174.14\). Moreover, they know that \(\sigma_X = 20.65\) and \(\sigma_Y = 24.41\).

The interest of the study is in testing whether individuals on the first diet have different average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0987662320

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 345 male hickory shad (labeled \(X\)). Further, they take a sample of 223 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 38.77\) and \(\overline{Y} = 38.9\). Moreover, they know that \(\sigma_X = 3.37\) and \(\sigma_Y = 2.86\).

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0604239689

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 320 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 80 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3680.06\) and \(\overline{Y} = 3811.64\). Moreover, they know that \(\sigma_X = 530.78\) and \(\sigma_Y = 501.29\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0165475197

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 119 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 179 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 337.69\) and \(\overline{Y} = 316.03\). Moreover, they know that \(\sigma_X = 85.88\) and \(\sigma_Y = 29.14\).

The interest of the study is in testing whether individuals taking the first treatment differ in their average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0641807344

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 52 individuals on the first diet (labeled \(X\)). Further, they take a sample of 377 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 107.65\) and \(\overline{Y} = 103.9\). Moreover, they know that \(\sigma_X = 11.04\) and \(\sigma_Y = 12.44\).

The interest of the study is in testing whether individuals on the first diet have higher average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0981442141

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 359 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 119 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3774.65\) and \(\overline{Y} = 3817.73\). Moreover, they know that \(\sigma_X = 296.3\) and \(\sigma_Y = 792.3\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0533882029

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 164 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 275 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 2687\) and \(\overline{Y} = 2690.53\). Moreover, they know that \(\sigma_X = 92.32\) and \(\sigma_Y = 88.4\).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0574181227

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 211 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 40 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3297.15\) and \(\overline{Y} = 3424.98\). Moreover, they know that \(\sigma_X = 676.96\) and \(\sigma_Y = 355.49\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0055136291

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 51 individuals on the first diet (labeled \(X\)). Further, they take a sample of 251 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 120.24\) and \(\overline{Y} = 121.75\). Moreover, they know that \(\sigma_X = 7.81\) and \(\sigma_Y = 11.88\).

The interest of the study is in testing whether individuals on the first diet have lower average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0756817803

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 438 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 350 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.19\) and \(\overline{Y} = 34.21\). Moreover, they know that \(\sigma_X = 0.7176\) and \(\sigma_Y = 0.8039\).

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0743980545

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 385 male hickory shad (labeled \(X\)). Further, they take a sample of 287 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.29\) and \(\overline{Y} = 35.16\). Moreover, they know that \(\sigma_X = 4.75\) and \(\sigma_Y = 4.42\).

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0708973228

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 163 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 400 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 42.45\) and \(\overline{Y} = 40.99\). Moreover, they know that \(\sigma_X = 8.08\) and \(\sigma_Y = 9.27\).

The interest of the study is in testing whether students in Introductory Probability study for different lengths of time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0906104783

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 468 male hickory shad (labeled \(X\)). Further, they take a sample of 233 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 37.09\) and \(\overline{Y} = 36.9\). Moreover, they know that \(\sigma_X = 4.03\) and \(\sigma_Y = 3.05\).

The interest of the study is in testing whether male hickory shad have different average lengths (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0872104139

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 272 individuals on the first diet (labeled \(X\)). Further, they take a sample of 223 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 210.9\) and \(\overline{Y} = 204.88\). Moreover, they know that \(\sigma_X = 16.1\) and \(\sigma_Y = 48.16\).

The interest of the study is in testing whether individuals on the first diet have higher average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0833769499

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 290 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 326 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 681.8\) and \(\overline{Y} = 675.57\). Moreover, they know that \(\sigma_X = 43.22\) and \(\sigma_Y = 26.69\).

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0629411982

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 281 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 80 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 42.25\) and \(\overline{Y} = 42.67\). Moreover, they know that \(\sigma_X = 10.64\) and \(\sigma_Y = 8.12\).

The interest of the study is in testing whether students in Introductory Probability study for less time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0792206038

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 379 individuals from the first region (labeled \(X\)). Further, they take a sample of 51 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 166.61\) and \(\overline{Y} = 165.79\). Moreover, they know that \(\sigma_X = 6.76\) and \(\sigma_Y = 3.33\).

The interest of the study is in testing whether individuals from the first region are different height on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0405931000

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 313 male hickory shad (labeled \(X\)). Further, they take a sample of 462 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.93\) and \(\overline{Y} = 37.32\). Moreover, they know that \(\sigma_X = 3.57\) and \(\sigma_Y = 4.01\).

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0130701635

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 224 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 227 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 39.71\) and \(\overline{Y} = 38.67\). Moreover, they know that \(\sigma_X = 8.26\) and \(\sigma_Y = 5.2\).

The interest of the study is in testing whether students in Introductory Probability study for more time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0270597583

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 279 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 293 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 594.68\) and \(\overline{Y} = 592.29\). Moreover, they know that \(\sigma_X = 76.61\) and \(\sigma_Y = 79.14\).

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0458510174

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 100 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 437 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 119.27\) and \(\overline{Y} = 117.9\). Moreover, they know that \(\sigma_X = 10.9\) and \(\sigma_Y = 9.52\).

The interest of the study is in testing whether individuals taking the first medication have different average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0247671927

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 461 individuals from the first region (labeled \(X\)). Further, they take a sample of 200 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 159.49\) and \(\overline{Y} = 158.74\). Moreover, they know that \(\sigma_X = 5.49\) and \(\sigma_Y = 8.56\).

The interest of the study is in testing whether individuals from the first region are taller on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0318652294

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 123 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 371 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3777.39\) and \(\overline{Y} = 3754.85\). Moreover, they know that \(\sigma_X = 391.72\) and \(\sigma_Y = 615.11\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0894808159

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 296 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 189 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 24.58\) and \(\overline{Y} = 23.89\). Moreover, they know that \(\sigma_X = 13.95\) and \(\sigma_Y = 11.1\).

The interest of the study is in testing whether students in Introductory Probability study for different lengths of time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0750719740

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 214 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 265 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 7841\) and \(\overline{Y} = 7853.32\). Moreover, they know that \(\sigma_X = 228.52\) and \(\sigma_Y = 233.05\).

The interest of the study is in testing whether lightbulbs of the first model last for a different average length of time (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0576899291

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 218 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 171 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 9471\) and \(\overline{Y} = 9527.32\). Moreover, they know that \(\sigma_X = 452.25\) and \(\sigma_Y = 310.22\).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0441493429

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 377 individuals on the first diet (labeled \(X\)). Further, they take a sample of 335 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 108.92\) and \(\overline{Y} = 108.48\). Moreover, they know that \(\sigma_X = 10.89\) and \(\sigma_Y = 11.97\).

The interest of the study is in testing whether individuals on the first diet have higher average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0211642247

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 205 individuals on the first diet (labeled \(X\)). Further, they take a sample of 491 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 124.2\) and \(\overline{Y} = 124.75\). Moreover, they know that \(\sigma_X = 12.42\) and \(\sigma_Y = 12.54\).

The interest of the study is in testing whether individuals on the first diet have lower average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0519707356

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 200 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 320 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.64\) and \(\overline{Y} = 34.71\). Moreover, they know that \(\sigma_X = 0.9375\) and \(\sigma_Y = 1.443\).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0664291534

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 187 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 67 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 44.63\) and \(\overline{Y} = 47.59\). Moreover, they know that \(\sigma_X = 5.53\) and \(\sigma_Y = 10.51\).

The interest of the study is in testing whether students in Introductory Probability study for less time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0760975601

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 249 male hickory shad (labeled \(X\)). Further, they take a sample of 358 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 35.83\) and \(\overline{Y} = 36.49\). Moreover, they know that \(\sigma_X = 2.99\) and \(\sigma_Y = 3.94\).

The interest of the study is in testing whether male hickory shad have different average lengths (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0660926269

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 235 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 296 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 117.61\) and \(\overline{Y} = 116.14\). Moreover, they know that \(\sigma_X = 11.61\) and \(\sigma_Y = 10.1\).

The interest of the study is in testing whether individuals taking the first medication have higher average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0074158306

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 113 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 31 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 8875\) and \(\overline{Y} = 8785.03\). Moreover, they know that \(\sigma_X = 334.06\) and \(\sigma_Y = 380.83\).

The interest of the study is in testing whether lightbulbs of the first model last longer on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0828918224

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 177 male hickory shad (labeled \(X\)). Further, they take a sample of 424 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.79\) and \(\overline{Y} = 33.99\). Moreover, they know that \(\sigma_X = 4.61\) and \(\sigma_Y = 4.78\).

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0395232125

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 48 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 219 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 9634\) and \(\overline{Y} = 9702.47\). Moreover, they know that \(\sigma_X = 248.24\) and \(\sigma_Y = 473.35\).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0911937900

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 68 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 442 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3543.99\) and \(\overline{Y} = 3649.26\). Moreover, they know that \(\sigma_X = 326.59\) and \(\sigma_Y = 543.13\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0741040875

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 473 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 262 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 103.38\) and \(\overline{Y} = 104.45\). Moreover, they know that \(\sigma_X = 11.57\) and \(\sigma_Y = 10.86\).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0431270184

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 389 individuals on the first diet (labeled \(X\)). Further, they take a sample of 118 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 183.07\) and \(\overline{Y} = 182.61\). Moreover, they know that \(\sigma_X = 42.8\) and \(\sigma_Y = 17.55\).

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0290440529

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 191 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 386 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 44.95\) and \(\overline{Y} = 47\). Moreover, they know that \(\sigma_X = 14.64\) and \(\sigma_Y = 8.21\).

The interest of the study is in testing whether students in Introductory Probability study for different lengths of time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0639054888

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 284 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 411 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.05\) and \(\overline{Y} = 36.05\). Moreover, they know that \(\sigma_X = 0.7906\) and \(\sigma_Y = 0.6597\).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0403342625

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 166 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 46 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 103.02\) and \(\overline{Y} = 102.83\). Moreover, they know that \(\sigma_X = 8.53\) and \(\sigma_Y = 10.16\).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0420442811

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 171 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 347 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.38\) and \(\overline{Y} = 33.47\). Moreover, they know that \(\sigma_X = 0.6005\) and \(\sigma_Y = 0.6504\).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0376752393

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 108 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 47 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3682.96\) and \(\overline{Y} = 3799.77\). Moreover, they know that \(\sigma_X = 413.11\) and \(\sigma_Y = 446.84\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0895372549

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 207 individuals on the first diet (labeled \(X\)). Further, they take a sample of 336 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 122.02\) and \(\overline{Y} = 121.56\). Moreover, they know that \(\sigma_X = 10.77\) and \(\sigma_Y = 7.74\).

The interest of the study is in testing whether individuals on the first diet have different average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0557618415

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 71 male hickory shad (labeled \(X\)). Further, they take a sample of 174 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.32\) and \(\overline{Y} = 34.02\). Moreover, they know that \(\sigma_X = 2.76\) and \(\sigma_Y = 3.8\).

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0910554964

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 458 male hickory shad (labeled \(X\)). Further, they take a sample of 294 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 37.19\) and \(\overline{Y} = 36.97\). Moreover, they know that \(\sigma_X = 3.14\) and \(\sigma_Y = 4.29\).

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0675525932

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 38 individuals on the first diet (labeled \(X\)). Further, they take a sample of 306 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 202.29\) and \(\overline{Y} = 204.54\). Moreover, they know that \(\sigma_X = 28.32\) and \(\sigma_Y = 34.08\).

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0024147957

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 473 individuals on the first diet (labeled \(X\)). Further, they take a sample of 132 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 123.14\) and \(\overline{Y} = 121.01\). Moreover, they know that \(\sigma_X = 11.73\) and \(\sigma_Y = 9.41\).

The interest of the study is in testing whether individuals on the first diet have different average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0417602831

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 363 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 183 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3491.87\) and \(\overline{Y} = 3374.22\). Moreover, they know that \(\sigma_X = 452.03\) and \(\sigma_Y = 761.11\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0894729400

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 470 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 494 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 25.87\) and \(\overline{Y} = 26.31\). Moreover, they know that \(\sigma_X = 13.83\) and \(\sigma_Y = 7.97\).

The interest of the study is in testing whether students in Introductory Probability study for more time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0218291173

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 402 individuals on the first diet (labeled \(X\)). Further, they take a sample of 219 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 156.75\) and \(\overline{Y} = 158.51\). Moreover, they know that \(\sigma_X = 46.59\) and \(\sigma_Y = 41.39\).

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0379421656

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 462 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 110 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3081.05\) and \(\overline{Y} = 3082.06\). Moreover, they know that \(\sigma_X = 339.23\) and \(\sigma_Y = 503.12\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0393239811

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 93 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 123 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3471.68\) and \(\overline{Y} = 3513.85\). Moreover, they know that \(\sigma_X = 760.96\) and \(\sigma_Y = 365.99\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0791249784

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 129 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 469 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 103.73\) and \(\overline{Y} = 104.73\). Moreover, they know that \(\sigma_X = 8.13\) and \(\sigma_Y = 10.43\).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0797506956

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 475 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 412 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 105.34\) and \(\overline{Y} = 103.58\). Moreover, they know that \(\sigma_X = 11.71\) and \(\sigma_Y = 7.86\).

The interest of the study is in testing whether individuals taking the first medication have higher average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0130356548

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 58 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 116 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 35.72\) and \(\overline{Y} = 33.07\). Moreover, they know that \(\sigma_X = 10.24\) and \(\sigma_Y = 7.31\).

The interest of the study is in testing whether students in Introductory Probability study for more time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0804682754

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 250 individuals from the first region (labeled \(X\)). Further, they take a sample of 374 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 176.03\) and \(\overline{Y} = 175.29\). Moreover, they know that \(\sigma_X = 9.1\) and \(\sigma_Y = 3.44\).

The interest of the study is in testing whether individuals from the first region are shorter on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0293199941

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 257 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 257 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 37.19\) and \(\overline{Y} = 37.3\). Moreover, they know that \(\sigma_X = 0.8137\) and \(\sigma_Y = 0.5021\).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0576717591

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 146 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 85 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 4717\) and \(\overline{Y} = 4774.65\). Moreover, they know that \(\sigma_X = 157.07\) and \(\sigma_Y = 223.33\).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0945248435

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 94 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 217 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.07\) and \(\overline{Y} = 33.42\). Moreover, they know that \(\sigma_X = 1.0785\) and \(\sigma_Y = 1.1422\).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0209248697

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 277 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 160 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 123.58\) and \(\overline{Y} = 121.68\). Moreover, they know that \(\sigma_X = 7.65\) and \(\sigma_Y = 10.7\).

The interest of the study is in testing whether individuals taking the first medication have higher average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0327931578

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 131 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 154 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 2246\) and \(\overline{Y} = 2250.53\). Moreover, they know that \(\sigma_X = 90.66\) and \(\sigma_Y = 103.63\).

The interest of the study is in testing whether lightbulbs of the first model last longer on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0215513076

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 427 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 223 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.99\) and \(\overline{Y} = 36.94\). Moreover, they know that \(\sigma_X = 0.9938\) and \(\sigma_Y = 0.7159\).

The interest of the study is in testing whether individuals taking the first medication have higher average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0339883132

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 86 male hickory shad (labeled \(X\)). Further, they take a sample of 165 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 32.71\) and \(\overline{Y} = 32.76\). Moreover, they know that \(\sigma_X = 2.15\) and \(\sigma_Y = 2.6\).

The interest of the study is in testing whether male hickory shad have different average lengths (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0645507230

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 348 individuals from the first region (labeled \(X\)). Further, they take a sample of 342 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 173.1\) and \(\overline{Y} = 174.52\). Moreover, they know that \(\sigma_X = 5.38\) and \(\sigma_Y = 9.76\).

The interest of the study is in testing whether individuals from the first region are shorter on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0368433757

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 381 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 391 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 125.18\) and \(\overline{Y} = 127.5\). Moreover, they know that \(\sigma_X = 12.36\) and \(\sigma_Y = 7.93\).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0323534374

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 171 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 479 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3402.07\) and \(\overline{Y} = 3402.35\). Moreover, they know that \(\sigma_X = 716.22\) and \(\sigma_Y = 290.56\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0253574991

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 323 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 388 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 106.61\) and \(\overline{Y} = 107.56\). Moreover, they know that \(\sigma_X = 7.2\) and \(\sigma_Y = 9.15\).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0153824341

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 256 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 190 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 113.13\) and \(\overline{Y} = 111.63\). Moreover, they know that \(\sigma_X = 11.13\) and \(\sigma_Y = 12.39\).

The interest of the study is in testing whether individuals taking the first medication have higher average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0148509110

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 369 individuals on the first diet (labeled \(X\)). Further, they take a sample of 448 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 201.14\) and \(\overline{Y} = 206.07\). Moreover, they know that \(\sigma_X = 46.56\) and \(\sigma_Y = 26.14\).

The interest of the study is in testing whether individuals on the first diet have different average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0740283251

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 434 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 63 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 35.29\) and \(\overline{Y} = 34.87\). Moreover, they know that \(\sigma_X = 1.0133\) and \(\sigma_Y = 1.188\).

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0535501705

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 207 individuals in the first population (labeled \(X\)). Further, they take a sample of 386 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 5.37\) and \(\overline{Y} = 5.46\). Moreover, they know that \(\sigma_X = 0.6383\) and \(\sigma_Y = 0.6405\).

The interest of the study is in testing whether individuals in the first population have lower average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0853555287

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 272 male hickory shad (labeled \(X\)). Further, they take a sample of 359 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.78\) and \(\overline{Y} = 34.33\). Moreover, they know that \(\sigma_X = 2.53\) and \(\sigma_Y = 3.7\).

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0888784942

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 221 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 283 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 461.9\) and \(\overline{Y} = 460.04\). Moreover, they know that \(\sigma_X = 71.93\) and \(\sigma_Y = 47.18\).

The interest of the study is in testing whether individuals taking the first treatment have shorter average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0142732120

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 75 male hickory shad (labeled \(X\)). Further, they take a sample of 384 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.03\) and \(\overline{Y} = 33.99\). Moreover, they know that \(\sigma_X = 4.47\) and \(\sigma_Y = 2.29\).

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0215452825

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 227 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 272 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3583.8\) and \(\overline{Y} = 3597.34\). Moreover, they know that \(\sigma_X = 463.82\) and \(\sigma_Y = 543.42\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0893964100

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 167 individuals from the first region (labeled \(X\)). Further, they take a sample of 217 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 159.98\) and \(\overline{Y} = 161.28\). Moreover, they know that \(\sigma_X = 6.01\) and \(\sigma_Y = 9.72\).

The interest of the study is in testing whether individuals from the first region are shorter on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0280856921

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 91 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 47 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 38.27\) and \(\overline{Y} = 32.61\). Moreover, they know that \(\sigma_X = 7.14\) and \(\sigma_Y = 11.45\).

The interest of the study is in testing whether students in Introductory Probability study for more time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0254308819

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 433 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 381 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.51\) and \(\overline{Y} = 34.58\). Moreover, they know that \(\sigma_X = 0.9515\) and \(\sigma_Y = 0.715\).

The interest of the study is in testing whether individuals taking the first medication have higher average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0105779456

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 125 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 499 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3158.97\) and \(\overline{Y} = 3176.13\). Moreover, they know that \(\sigma_X = 736.55\) and \(\sigma_Y = 470.28\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0385623603

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 366 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 60 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 111.14\) and \(\overline{Y} = 109.78\). Moreover, they know that \(\sigma_X = 8.26\) and \(\sigma_Y = 9.07\).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0150614231

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 345 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 52 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 37.2\) and \(\overline{Y} = 37.41\). Moreover, they know that \(\sigma_X = 1.1913\) and \(\sigma_Y = 0.9332\).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0818284031

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 122 male hickory shad (labeled \(X\)). Further, they take a sample of 129 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 30.63\) and \(\overline{Y} = 31.29\). Moreover, they know that \(\sigma_X = 2.24\) and \(\sigma_Y = 3.26\).

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0588040836

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 317 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 139 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 707.13\) and \(\overline{Y} = 711.12\). Moreover, they know that \(\sigma_X = 37.42\) and \(\sigma_Y = 27.02\).

The interest of the study is in testing whether individuals taking the first treatment have shorter average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0729212122

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 317 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 366 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 46.32\) and \(\overline{Y} = 47.54\). Moreover, they know that \(\sigma_X = 12.39\) and \(\sigma_Y = 8.79\).

The interest of the study is in testing whether students in Introductory Probability study for less time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0844828538

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 139 male hickory shad (labeled \(X\)). Further, they take a sample of 180 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 39.62\) and \(\overline{Y} = 39.78\). Moreover, they know that \(\sigma_X = 2.35\) and \(\sigma_Y = 3.52\).

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0757353256

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 231 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 404 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.3\) and \(\overline{Y} = 33.24\). Moreover, they know that \(\sigma_X = 1.2616\) and \(\sigma_Y = 0.5347\).

The interest of the study is in testing whether individuals taking the first medication have higher average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0153633123

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 112 individuals from the first region (labeled \(X\)). Further, they take a sample of 216 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 172.86\) and \(\overline{Y} = 174.04\). Moreover, they know that \(\sigma_X = 3.6\) and \(\sigma_Y = 5.77\).

The interest of the study is in testing whether individuals from the first region are different height on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0270790347

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 242 individuals in the first population (labeled \(X\)). Further, they take a sample of 266 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 4.82\) and \(\overline{Y} = 4.8\). Moreover, they know that \(\sigma_X = 0.5443\) and \(\sigma_Y = 0.2862\).

The interest of the study is in testing whether individuals in the first population differ in their average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0963338615

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 165 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 250 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.91\) and \(\overline{Y} = 33.8\). Moreover, they know that \(\sigma_X = 0.5228\) and \(\sigma_Y = 0.7609\).

The interest of the study is in testing whether individuals taking the first medication have higher average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0969466625

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 92 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 139 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.92\) and \(\overline{Y} = 33.65\). Moreover, they know that \(\sigma_X = 1.2765\) and \(\sigma_Y = 1.2705\).

The interest of the study is in testing whether individuals taking the first medication have higher average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0523108030

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 101 individuals in the first population (labeled \(X\)). Further, they take a sample of 403 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3.43\) and \(\overline{Y} = 3.35\). Moreover, they know that \(\sigma_X = 0.3798\) and \(\sigma_Y = 0.2165\).

The interest of the study is in testing whether individuals in the first population have higher average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0656555113

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 221 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 487 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3632.62\) and \(\overline{Y} = 3567.73\). Moreover, they know that \(\sigma_X = 385.33\) and \(\sigma_Y = 599.69\).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0511751854

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 322 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 166 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 37.71\) and \(\overline{Y} = 40.14\). Moreover, they know that \(\sigma_X = 11.8\) and \(\sigma_Y = 11.42\).

The interest of the study is in testing whether students in Introductory Probability study for less time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0671673696

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 303 individuals on the first diet (labeled \(X\)). Further, they take a sample of 443 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 167.42\) and \(\overline{Y} = 164\). Moreover, they know that \(\sigma_X = 30.75\) and \(\sigma_Y = 16.91\).

The interest of the study is in testing whether individuals on the first diet have higher average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0999155372

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 451 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 351 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 796.22\) and \(\overline{Y} = 811.05\). Moreover, they know that \(\sigma_X = 31.39\) and \(\sigma_Y = 92.45\).

The interest of the study is in testing whether individuals taking the first treatment have shorter average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0903240932

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 484 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 369 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 2127\) and \(\overline{Y} = 2136.09\). Moreover, they know that \(\sigma_X = 96.22\) and \(\sigma_Y = 68.8\).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0990773534

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 104 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 230 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 410.24\) and \(\overline{Y} = 403.21\). Moreover, they know that \(\sigma_X = 35.23\) and \(\sigma_Y = 66.96\).

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0123795565

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 68 individuals on the first diet (labeled \(X\)). Further, they take a sample of 250 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 111.04\) and \(\overline{Y} = 110.29\). Moreover, they know that \(\sigma_X = 10.52\) and \(\sigma_Y = 7.9\).

The interest of the study is in testing whether individuals on the first diet have lower average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0428424403

Self Assessment 16.2

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 454 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 239 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 110.36\) (with sample standard deviation \(7.28\)) and \(\overline{Y} = 110.88\) (with sample standard deviation \(9.75\)).

The interest of the study is in testing whether individuals taking the first medication have different average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 453 degrees of freedom.A \(t\) distribution with 238 degrees of freedom.A \(t\) distribution with 380.962 degrees of freedom.A \(t\) distribution with 691 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0271411425

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 252 individuals on the first diet (labeled \(X\)). Further, they take a sample of 486 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 123.65\) (with sample standard deviation \(12.56\)) and \(\overline{Y} = 123.38\) (with sample standard deviation \(11.65\)).

The interest of the study is in testing whether individuals on the first diet have different average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 475.884 degrees of freedom.A standard normal distribution.A \(t\) distribution with 736 degrees of freedom.A \(t\) distribution with 485 degrees of freedom.A \(t\) distribution with 251 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0013716585

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 59 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 256 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.42\) (with sample standard deviation \(1.4095\)) and \(\overline{Y} = 36.41\) (with sample standard deviation \(1.3053\)).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 58 degrees of freedom.A \(t\) distribution with 82.461 degrees of freedom.A \(t\) distribution with 313 degrees of freedom.A standard normal distribution.A \(t\) distribution with 255 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0588217085

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 388 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 320 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 125.02\) (with sample standard deviation \(12.29\)) and \(\overline{Y} = 125.9\) (with sample standard deviation \(10.1\)).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 705.992 degrees of freedom.A \(t\) distribution with 387 degrees of freedom.A \(t\) distribution with 706 degrees of freedom.A standard normal distribution.A \(t\) distribution with 319 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0768195763

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 168 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 329 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3169.22\) (with sample standard deviation \(757.33\)) and \(\overline{Y} = 3194.66\) (with sample standard deviation \(353.46\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 495 degrees of freedom.A \(t\) distribution with 167 degrees of freedom.A standard normal distribution.A \(t\) distribution with 328 degrees of freedom.A \(t\) distribution with 204.926 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0420993555

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 365 individuals on the first diet (labeled \(X\)). Further, they take a sample of 479 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 105.07\) (with sample standard deviation \(10.74\)) and \(\overline{Y} = 104.38\) (with sample standard deviation \(10.26\)).

The interest of the study is in testing whether individuals on the first diet have different average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 478 degrees of freedom.A \(t\) distribution with 364 degrees of freedom.A \(t\) distribution with 842 degrees of freedom.A \(t\) distribution with 764.685 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0057087731

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 286 individuals from the first region (labeled \(X\)). Further, they take a sample of 305 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 176.83\) (with sample standard deviation \(5.84\)) and \(\overline{Y} = 177.69\) (with sample standard deviation \(8.98\)).

The interest of the study is in testing whether individuals from the first region are different height on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 285 degrees of freedom.A \(t\) distribution with 304 degrees of freedom.A standard normal distribution.A \(t\) distribution with 589 degrees of freedom.A \(t\) distribution with 525.944 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0436922720

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 397 individuals from the first region (labeled \(X\)). Further, they take a sample of 266 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 162.18\) (with sample standard deviation \(4.1\)) and \(\overline{Y} = 162.54\) (with sample standard deviation \(6.66\)).

The interest of the study is in testing whether individuals from the first region are taller on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 265 degrees of freedom.A standard normal distribution.A \(t\) distribution with 661 degrees of freedom.A \(t\) distribution with 399.434 degrees of freedom.A \(t\) distribution with 396 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0874597441

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 451 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 131 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 2733\) (with sample standard deviation \(98.1\)) and \(\overline{Y} = 2743.88\) (with sample standard deviation \(90.01\)).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 580 degrees of freedom.A \(t\) distribution with 227.363 degrees of freedom.A \(t\) distribution with 450 degrees of freedom.A \(t\) distribution with 130 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0764164229

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 351 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 235 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 6450\) (with sample standard deviation \(274.11\)) and \(\overline{Y} = 6504.71\) (with sample standard deviation \(264.74\)).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 234 degrees of freedom.A \(t\) distribution with 513.569 degrees of freedom.A \(t\) distribution with 584 degrees of freedom.A \(t\) distribution with 350 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0893337190

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 358 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 334 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.14\) (with sample standard deviation \(1.0313\)) and \(\overline{Y} = 36.09\) (with sample standard deviation \(0.5426\)).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 548.508 degrees of freedom.A \(t\) distribution with 333 degrees of freedom.A \(t\) distribution with 690 degrees of freedom.A standard normal distribution.A \(t\) distribution with 357 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0381626601

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 405 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 350 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 6042\) (with sample standard deviation \(162.13\)) and \(\overline{Y} = 6039.13\) (with sample standard deviation \(231.11\)).

The interest of the study is in testing whether lightbulbs of the first model last longer on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 753 degrees of freedom.A \(t\) distribution with 404 degrees of freedom.A \(t\) distribution with 349 degrees of freedom.A standard normal distribution.A \(t\) distribution with 613.178 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0853304120

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 398 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 396 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 37.89\) (with sample standard deviation \(1.0837\)) and \(\overline{Y} = 37.98\) (with sample standard deviation \(1.2115\)).

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 792 degrees of freedom.A \(t\) distribution with 395 degrees of freedom.A standard normal distribution.A \(t\) distribution with 781.479 degrees of freedom.A \(t\) distribution with 397 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0458976775

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 447 individuals on the first diet (labeled \(X\)). Further, they take a sample of 58 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 217.93\) (with sample standard deviation \(17.58\)) and \(\overline{Y} = 215.76\) (with sample standard deviation \(28.7\)).

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 62.666 degrees of freedom.A \(t\) distribution with 503 degrees of freedom.A standard normal distribution.A \(t\) distribution with 57 degrees of freedom.A \(t\) distribution with 446 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0745759200

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 89 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 268 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 31.51\) (with sample standard deviation \(11.4\)) and \(\overline{Y} = 30.99\) (with sample standard deviation \(7.92\)).

The interest of the study is in testing whether students in Introductory Probability study for less time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 88 degrees of freedom.A \(t\) distribution with 355 degrees of freedom.A \(t\) distribution with 117.476 degrees of freedom.A \(t\) distribution with 267 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0055926874

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 87 individuals from the first region (labeled \(X\)). Further, they take a sample of 343 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 173.4\) (with sample standard deviation \(9.06\)) and \(\overline{Y} = 175.76\) (with sample standard deviation \(9.66\)).

The interest of the study is in testing whether individuals from the first region are different height on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 342 degrees of freedom.A standard normal distribution.A \(t\) distribution with 428 degrees of freedom.A \(t\) distribution with 139.824 degrees of freedom.A \(t\) distribution with 86 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0189945244

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 379 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 268 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 7901\) (with sample standard deviation \(316.23\)) and \(\overline{Y} = 7839.9\) (with sample standard deviation \(327.17\)).

The interest of the study is in testing whether lightbulbs of the first model last for a different average length of time (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 378 degrees of freedom.A \(t\) distribution with 645 degrees of freedom.A \(t\) distribution with 267 degrees of freedom.A standard normal distribution.A \(t\) distribution with 562.804 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0600899560

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 274 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 67 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 22.52\) (with sample standard deviation \(5.85\)) and \(\overline{Y} = 22.5\) (with sample standard deviation \(6.92\)).

The interest of the study is in testing whether students in Introductory Probability study for more time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 273 degrees of freedom.A \(t\) distribution with 339 degrees of freedom.A \(t\) distribution with 90.415 degrees of freedom.A \(t\) distribution with 66 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0988860440

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 181 individuals on the first diet (labeled \(X\)). Further, they take a sample of 362 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 110.12\) (with sample standard deviation \(11.21\)) and \(\overline{Y} = 112.29\) (with sample standard deviation \(12.84\)).

The interest of the study is in testing whether individuals on the first diet have different average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 541 degrees of freedom.A \(t\) distribution with 180 degrees of freedom.A \(t\) distribution with 361 degrees of freedom.A \(t\) distribution with 406.409 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0423137359

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 473 individuals from the first region (labeled \(X\)). Further, they take a sample of 152 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 173.39\) (with sample standard deviation \(7.14\)) and \(\overline{Y} = 175.06\) (with sample standard deviation \(6.24\)).

The interest of the study is in testing whether individuals from the first region are shorter on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 472 degrees of freedom.A \(t\) distribution with 151 degrees of freedom.A \(t\) distribution with 288.457 degrees of freedom.A standard normal distribution.A \(t\) distribution with 623 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0513932405

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 82 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 404 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 335.27\) (with sample standard deviation \(24.14\)) and \(\overline{Y} = 343.31\) (with sample standard deviation \(26.94\)).

The interest of the study is in testing whether individuals taking the first treatment differ in their average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 81 degrees of freedom.A \(t\) distribution with 484 degrees of freedom.A \(t\) distribution with 125.515 degrees of freedom.A standard normal distribution.A \(t\) distribution with 403 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0808947590

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 52 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 380 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3620.72\) (with sample standard deviation \(231.63\)) and \(\overline{Y} = 3686.89\) (with sample standard deviation \(720.62\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 222.936 degrees of freedom.A standard normal distribution.A \(t\) distribution with 51 degrees of freedom.A \(t\) distribution with 379 degrees of freedom.A \(t\) distribution with 430 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0532808862

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 41 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 303 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 5670\) (with sample standard deviation \(161.88\)) and \(\overline{Y} = 5616.71\) (with sample standard deviation \(166.53\)).

The interest of the study is in testing whether lightbulbs of the first model last for a different average length of time (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 52.135 degrees of freedom.A \(t\) distribution with 302 degrees of freedom.A \(t\) distribution with 342 degrees of freedom.A \(t\) distribution with 40 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0653749782

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 384 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 484 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 519.85\) (with sample standard deviation \(96.43\)) and \(\overline{Y} = 530.29\) (with sample standard deviation \(86.54\)).

The interest of the study is in testing whether individuals taking the first treatment differ in their average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 866 degrees of freedom.A \(t\) distribution with 483 degrees of freedom.A standard normal distribution.A \(t\) distribution with 383 degrees of freedom.A \(t\) distribution with 777.21 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0355102259

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 131 individuals in the first population (labeled \(X\)). Further, they take a sample of 93 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 4.97\) (with sample standard deviation \(0.584\)) and \(\overline{Y} = 5.12\) (with sample standard deviation \(0.331\)).

The interest of the study is in testing whether individuals in the first population have lower average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 130 degrees of freedom.A standard normal distribution.A \(t\) distribution with 222 degrees of freedom.A \(t\) distribution with 92 degrees of freedom.A \(t\) distribution with 212.722 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0891811403

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 164 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 446 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3115.32\) (with sample standard deviation \(481.59\)) and \(\overline{Y} = 3154.12\) (with sample standard deviation \(524.67\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 445 degrees of freedom.A \(t\) distribution with 163 degrees of freedom.A standard normal distribution.A \(t\) distribution with 608 degrees of freedom.A \(t\) distribution with 314.393 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0972788241

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 269 individuals on the first diet (labeled \(X\)). Further, they take a sample of 361 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 152.71\) (with sample standard deviation \(29.95\)) and \(\overline{Y} = 147.41\) (with sample standard deviation \(41.78\)).

The interest of the study is in testing whether individuals on the first diet have different average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 628 degrees of freedom.A \(t\) distribution with 627.113 degrees of freedom.A \(t\) distribution with 360 degrees of freedom.A standard normal distribution.A \(t\) distribution with 268 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0861281627

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 327 male hickory shad (labeled \(X\)). Further, they take a sample of 71 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.31\) (with sample standard deviation \(3.39\)) and \(\overline{Y} = 33\) (with sample standard deviation \(3.39\)).

The interest of the study is in testing whether male hickory shad have different average lengths (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 396 degrees of freedom.A \(t\) distribution with 102.658 degrees of freedom.A \(t\) distribution with 326 degrees of freedom.A \(t\) distribution with 70 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0901613744

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 163 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 138 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 102.23\) (with sample standard deviation \(10.64\)) and \(\overline{Y} = 99.78\) (with sample standard deviation \(9.54\)).

The interest of the study is in testing whether individuals taking the first medication have higher average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 298 degrees of freedom.A \(t\) distribution with 299 degrees of freedom.A \(t\) distribution with 162 degrees of freedom.A standard normal distribution.A \(t\) distribution with 137 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0161631886

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 355 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 326 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.85\) (with sample standard deviation \(1.183\)) and \(\overline{Y} = 36.77\) (with sample standard deviation \(1.4305\)).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 632.407 degrees of freedom.A standard normal distribution.A \(t\) distribution with 354 degrees of freedom.A \(t\) distribution with 679 degrees of freedom.A \(t\) distribution with 325 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0063352356

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 407 individuals on the first diet (labeled \(X\)). Further, they take a sample of 310 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 122.34\) (with sample standard deviation \(12.23\)) and \(\overline{Y} = 123.75\) (with sample standard deviation \(11.74\)).

The interest of the study is in testing whether individuals on the first diet have different average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 715 degrees of freedom.A \(t\) distribution with 309 degrees of freedom.A \(t\) distribution with 406 degrees of freedom.A \(t\) distribution with 678.254 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0415767968

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 150 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 336 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 212.76\) (with sample standard deviation \(74.64\)) and \(\overline{Y} = 196.51\) (with sample standard deviation \(44.12\)).

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 149 degrees of freedom.A \(t\) distribution with 484 degrees of freedom.A \(t\) distribution with 196.977 degrees of freedom.A \(t\) distribution with 335 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0292678023

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 436 male hickory shad (labeled \(X\)). Further, they take a sample of 430 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.22\) (with sample standard deviation \(3.72\)) and \(\overline{Y} = 34.48\) (with sample standard deviation \(4.12\)).

The interest of the study is in testing whether male hickory shad have different average lengths (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 864 degrees of freedom.A \(t\) distribution with 852.611 degrees of freedom.A \(t\) distribution with 435 degrees of freedom.A \(t\) distribution with 429 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0091065955

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 499 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 63 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.52\) (with sample standard deviation \(1.3753\)) and \(\overline{Y} = 33.3\) (with sample standard deviation \(0.7667\)).

The interest of the study is in testing whether individuals taking the first medication have higher average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 62 degrees of freedom.A \(t\) distribution with 560 degrees of freedom.A \(t\) distribution with 498 degrees of freedom.A \(t\) distribution with 120.138 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0776174276

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 445 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 363 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 668.21\) (with sample standard deviation \(77.07\)) and \(\overline{Y} = 663.39\) (with sample standard deviation \(36.05\)).

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 656.219 degrees of freedom.A \(t\) distribution with 806 degrees of freedom.A \(t\) distribution with 362 degrees of freedom.A standard normal distribution.A \(t\) distribution with 444 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0394769158

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 394 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 138 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 13919\) (with sample standard deviation \(666.11\)) and \(\overline{Y} = 13824.67\) (with sample standard deviation \(588.73\)).

The interest of the study is in testing whether lightbulbs of the first model last for a different average length of time (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 137 degrees of freedom.A \(t\) distribution with 268.575 degrees of freedom.A \(t\) distribution with 530 degrees of freedom.A standard normal distribution.A \(t\) distribution with 393 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0287449550

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 321 individuals in the first population (labeled \(X\)). Further, they take a sample of 316 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 5.68\) (with sample standard deviation \(0.2079\)) and \(\overline{Y} = 5.69\) (with sample standard deviation \(0.4553\)).

The interest of the study is in testing whether individuals in the first population have higher average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 315 degrees of freedom.A \(t\) distribution with 439.361 degrees of freedom.A \(t\) distribution with 320 degrees of freedom.A \(t\) distribution with 635 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0372273482

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 447 individuals from the first region (labeled \(X\)). Further, they take a sample of 386 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 160.32\) (with sample standard deviation \(3.19\)) and \(\overline{Y} = 160.4\) (with sample standard deviation \(7.38\)).

The interest of the study is in testing whether individuals from the first region are shorter on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 446 degrees of freedom.A standard normal distribution.A \(t\) distribution with 507.844 degrees of freedom.A \(t\) distribution with 385 degrees of freedom.A \(t\) distribution with 831 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0224306338

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 158 male hickory shad (labeled \(X\)). Further, they take a sample of 353 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 35.4\) (with sample standard deviation \(3.03\)) and \(\overline{Y} = 35.46\) (with sample standard deviation \(2.99\)).

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 509 degrees of freedom.A \(t\) distribution with 298.399 degrees of freedom.A \(t\) distribution with 157 degrees of freedom.A \(t\) distribution with 352 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0179408438

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 307 individuals on the first diet (labeled \(X\)). Further, they take a sample of 43 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 108.8\) (with sample standard deviation \(7.73\)) and \(\overline{Y} = 108.11\) (with sample standard deviation \(7.21\)).

The interest of the study is in testing whether individuals on the first diet have lower average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 42 degrees of freedom.A \(t\) distribution with 306 degrees of freedom.A \(t\) distribution with 348 degrees of freedom.A \(t\) distribution with 56.412 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0843409702

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 128 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 41 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 108.29\) (with sample standard deviation \(10.62\)) and \(\overline{Y} = 108.98\) (with sample standard deviation \(8.49\)).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 83.535 degrees of freedom.A \(t\) distribution with 127 degrees of freedom.A \(t\) distribution with 167 degrees of freedom.A \(t\) distribution with 40 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0454934002

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 461 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 448 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 104.9\) (with sample standard deviation \(11.1\)) and \(\overline{Y} = 104.37\) (with sample standard deviation \(9.32\)).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 447 degrees of freedom.A \(t\) distribution with 888.374 degrees of freedom.A standard normal distribution.A \(t\) distribution with 460 degrees of freedom.A \(t\) distribution with 907 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0557623058

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 491 individuals from the first region (labeled \(X\)). Further, they take a sample of 330 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 158.6\) (with sample standard deviation \(9.91\)) and \(\overline{Y} = 158.66\) (with sample standard deviation \(5.37\)).

The interest of the study is in testing whether individuals from the first region are shorter on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 490 degrees of freedom.A \(t\) distribution with 819 degrees of freedom.A \(t\) distribution with 329 degrees of freedom.A \(t\) distribution with 787.741 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0276747050

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 128 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 243 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 37.5\) (with sample standard deviation \(0.9355\)) and \(\overline{Y} = 37.68\) (with sample standard deviation \(0.8543\)).

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 369 degrees of freedom.A \(t\) distribution with 127 degrees of freedom.A \(t\) distribution with 242 degrees of freedom.A \(t\) distribution with 238.891 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0059647182

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 182 individuals on the first diet (labeled \(X\)). Further, they take a sample of 110 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 179.91\) (with sample standard deviation \(39.59\)) and \(\overline{Y} = 186.56\) (with sample standard deviation \(24.61\)).

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 181 degrees of freedom.A standard normal distribution.A \(t\) distribution with 289.753 degrees of freedom.A \(t\) distribution with 290 degrees of freedom.A \(t\) distribution with 109 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0613836556

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 400 male hickory shad (labeled \(X\)). Further, they take a sample of 260 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 31.93\) (with sample standard deviation \(3.13\)) and \(\overline{Y} = 31.96\) (with sample standard deviation \(2.02\)).

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 657.974 degrees of freedom.A \(t\) distribution with 658 degrees of freedom.A \(t\) distribution with 399 degrees of freedom.A standard normal distribution.A \(t\) distribution with 259 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0103069349

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 119 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 422 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 10946\) (with sample standard deviation \(379.42\)) and \(\overline{Y} = 10879.62\) (with sample standard deviation \(535.78\)).

The interest of the study is in testing whether lightbulbs of the first model last longer on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 264.566 degrees of freedom.A standard normal distribution.A \(t\) distribution with 421 degrees of freedom.A \(t\) distribution with 118 degrees of freedom.A \(t\) distribution with 539 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0771201284

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 268 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 382 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.47\) (with sample standard deviation \(0.8806\)) and \(\overline{Y} = 34.49\) (with sample standard deviation \(1.0783\)).

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 381 degrees of freedom.A \(t\) distribution with 648 degrees of freedom.A \(t\) distribution with 267 degrees of freedom.A \(t\) distribution with 633.179 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0867244704

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 495 male hickory shad (labeled \(X\)). Further, they take a sample of 227 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 32.03\) (with sample standard deviation \(4.47\)) and \(\overline{Y} = 32.91\) (with sample standard deviation \(3.46\)).

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 555.48 degrees of freedom.A standard normal distribution.A \(t\) distribution with 226 degrees of freedom.A \(t\) distribution with 720 degrees of freedom.A \(t\) distribution with 494 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0161580177

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 72 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 417 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3509.15\) (with sample standard deviation \(456.54\)) and \(\overline{Y} = 3512.15\) (with sample standard deviation \(369.13\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 71 degrees of freedom.A \(t\) distribution with 87.742 degrees of freedom.A \(t\) distribution with 487 degrees of freedom.A \(t\) distribution with 416 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0649044043

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 320 individuals on the first diet (labeled \(X\)). Further, they take a sample of 108 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 161.78\) (with sample standard deviation \(41.51\)) and \(\overline{Y} = 155.91\) (with sample standard deviation \(16.07\)).

The interest of the study is in testing whether individuals on the first diet have higher average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 418.93 degrees of freedom.A \(t\) distribution with 319 degrees of freedom.A \(t\) distribution with 426 degrees of freedom.A \(t\) distribution with 107 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0819891819

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 298 male hickory shad (labeled \(X\)). Further, they take a sample of 241 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 38.77\) (with sample standard deviation \(4.81\)) and \(\overline{Y} = 38.39\) (with sample standard deviation \(4.4\)).

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 537 degrees of freedom.A \(t\) distribution with 528.881 degrees of freedom.A standard normal distribution.A \(t\) distribution with 240 degrees of freedom.A \(t\) distribution with 297 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0698619477

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 76 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 139 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3796.67\) (with sample standard deviation \(479.58\)) and \(\overline{Y} = 3747.2\) (with sample standard deviation \(313.83\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 110.927 degrees of freedom.A \(t\) distribution with 138 degrees of freedom.A standard normal distribution.A \(t\) distribution with 213 degrees of freedom.A \(t\) distribution with 75 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0627890314

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 85 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 143 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3381.95\) (with sample standard deviation \(443.99\)) and \(\overline{Y} = 3383.57\) (with sample standard deviation \(517.04\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 197.926 degrees of freedom.A \(t\) distribution with 226 degrees of freedom.A \(t\) distribution with 84 degrees of freedom.A \(t\) distribution with 142 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0405633683

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 342 male hickory shad (labeled \(X\)). Further, they take a sample of 286 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.41\) (with sample standard deviation \(4.86\)) and \(\overline{Y} = 35.01\) (with sample standard deviation \(3.37\)).

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 606.114 degrees of freedom.A \(t\) distribution with 285 degrees of freedom.A \(t\) distribution with 341 degrees of freedom.A \(t\) distribution with 626 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0909775324

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 487 male hickory shad (labeled \(X\)). Further, they take a sample of 61 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 39.24\) (with sample standard deviation \(3.8\)) and \(\overline{Y} = 39.39\) (with sample standard deviation \(4.52\)).

The interest of the study is in testing whether male hickory shad have different average lengths (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 546 degrees of freedom.A \(t\) distribution with 60 degrees of freedom.A \(t\) distribution with 71.025 degrees of freedom.A \(t\) distribution with 486 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0553699829

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 170 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 95 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 110.43\) (with sample standard deviation \(9.64\)) and \(\overline{Y} = 111.88\) (with sample standard deviation \(12.09\)).

The interest of the study is in testing whether individuals taking the first medication have different average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 161.332 degrees of freedom.A standard normal distribution.A \(t\) distribution with 169 degrees of freedom.A \(t\) distribution with 263 degrees of freedom.A \(t\) distribution with 94 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0765170297

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 232 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 436 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 116.63\) (with sample standard deviation \(10.68\)) and \(\overline{Y} = 116.34\) (with sample standard deviation \(12.76\)).

The interest of the study is in testing whether individuals taking the first medication have different average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 547.461 degrees of freedom.A \(t\) distribution with 435 degrees of freedom.A \(t\) distribution with 231 degrees of freedom.A standard normal distribution.A \(t\) distribution with 666 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0094478703

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 273 individuals from the first region (labeled \(X\)). Further, they take a sample of 239 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 159.3\) (with sample standard deviation \(5.42\)) and \(\overline{Y} = 160.2\) (with sample standard deviation \(3.8\)).

The interest of the study is in testing whether individuals from the first region are different height on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 272 degrees of freedom.A \(t\) distribution with 487.537 degrees of freedom.A standard normal distribution.A \(t\) distribution with 510 degrees of freedom.A \(t\) distribution with 238 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0985302000

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 468 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 171 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 123.6\) (with sample standard deviation \(12.38\)) and \(\overline{Y} = 124.46\) (with sample standard deviation \(7.79\)).

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 637 degrees of freedom.A \(t\) distribution with 467 degrees of freedom.A \(t\) distribution with 170 degrees of freedom.A \(t\) distribution with 479.793 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0540990918

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 84 individuals from the first region (labeled \(X\)). Further, they take a sample of 409 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 171.46\) (with sample standard deviation \(7.47\)) and \(\overline{Y} = 171.45\) (with sample standard deviation \(6.48\)).

The interest of the study is in testing whether individuals from the first region are taller on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 491 degrees of freedom.A \(t\) distribution with 408 degrees of freedom.A \(t\) distribution with 110.103 degrees of freedom.A standard normal distribution.A \(t\) distribution with 83 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0026558196

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 89 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 91 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3163.36\) (with sample standard deviation \(729.34\)) and \(\overline{Y} = 3439.85\) (with sample standard deviation \(765.22\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 177.883 degrees of freedom.A standard normal distribution.A \(t\) distribution with 90 degrees of freedom.A \(t\) distribution with 88 degrees of freedom.A \(t\) distribution with 178 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0942444052

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 188 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 381 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 47.41\) (with sample standard deviation \(10.04\)) and \(\overline{Y} = 48.78\) (with sample standard deviation \(12.43\)).

The interest of the study is in testing whether students in Introductory Probability study for different lengths of time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 450.125 degrees of freedom.A \(t\) distribution with 380 degrees of freedom.A \(t\) distribution with 187 degrees of freedom.A \(t\) distribution with 567 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0277324740

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 491 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 259 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 2234\) (with sample standard deviation \(91.44\)) and \(\overline{Y} = 2226.2\) (with sample standard deviation \(77.14\)).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 606.699 degrees of freedom.A \(t\) distribution with 748 degrees of freedom.A \(t\) distribution with 258 degrees of freedom.A \(t\) distribution with 490 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0149387574

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 468 male hickory shad (labeled \(X\)). Further, they take a sample of 336 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.32\) (with sample standard deviation \(3.23\)) and \(\overline{Y} = 36.02\) (with sample standard deviation \(4.42\)).

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 579.967 degrees of freedom.A \(t\) distribution with 335 degrees of freedom.A \(t\) distribution with 802 degrees of freedom.A standard normal distribution.A \(t\) distribution with 467 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0109419755

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 210 individuals from the first region (labeled \(X\)). Further, they take a sample of 152 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 164.92\) (with sample standard deviation \(6.26\)) and \(\overline{Y} = 164.21\) (with sample standard deviation \(3.46\)).

The interest of the study is in testing whether individuals from the first region are taller on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 339.056 degrees of freedom.A \(t\) distribution with 360 degrees of freedom.A standard normal distribution.A \(t\) distribution with 209 degrees of freedom.A \(t\) distribution with 151 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0246712582

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 319 individuals on the first diet (labeled \(X\)). Further, they take a sample of 67 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 200.7\) (with sample standard deviation \(30.47\)) and \(\overline{Y} = 188.87\) (with sample standard deviation \(47.5\)).

The interest of the study is in testing whether individuals on the first diet have higher average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 384 degrees of freedom.A \(t\) distribution with 318 degrees of freedom.A standard normal distribution.A \(t\) distribution with 66 degrees of freedom.A \(t\) distribution with 77.781 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0831419668

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 372 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 477 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 113.39\) (with sample standard deviation \(8.78\)) and \(\overline{Y} = 114.27\) (with sample standard deviation \(9.05\)).

The interest of the study is in testing whether individuals taking the first medication have different average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 476 degrees of freedom.A \(t\) distribution with 371 degrees of freedom.A \(t\) distribution with 847 degrees of freedom.A \(t\) distribution with 808.099 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0567030656

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 481 individuals in the first population (labeled \(X\)). Further, they take a sample of 304 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 4.4\) (with sample standard deviation \(0.4033\)) and \(\overline{Y} = 4.29\) (with sample standard deviation \(0.6833\)).

The interest of the study is in testing whether individuals in the first population differ in their average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 783 degrees of freedom.A \(t\) distribution with 480 degrees of freedom.A \(t\) distribution with 437.718 degrees of freedom.A standard normal distribution.A \(t\) distribution with 303 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0930078301

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 74 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 319 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3770.56\) (with sample standard deviation \(647.91\)) and \(\overline{Y} = 3883.19\) (with sample standard deviation \(407.82\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 73 degrees of freedom.A \(t\) distribution with 86.867 degrees of freedom.A \(t\) distribution with 391 degrees of freedom.A \(t\) distribution with 318 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0409156640

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 496 male hickory shad (labeled \(X\)). Further, they take a sample of 344 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 31.46\) (with sample standard deviation \(3.75\)) and \(\overline{Y} = 32.08\) (with sample standard deviation \(3.22\)).

The interest of the study is in testing whether male hickory shad have different average lengths (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 495 degrees of freedom.A \(t\) distribution with 838 degrees of freedom.A \(t\) distribution with 800.796 degrees of freedom.A standard normal distribution.A \(t\) distribution with 343 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0927995085

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 329 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 169 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 32.75\) (with sample standard deviation \(13.89\)) and \(\overline{Y} = 30.41\) (with sample standard deviation \(8.1\)).

The interest of the study is in testing whether students in Introductory Probability study for more time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 488.253 degrees of freedom.A \(t\) distribution with 328 degrees of freedom.A \(t\) distribution with 168 degrees of freedom.A \(t\) distribution with 496 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0596167919

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 222 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 358 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.05\) (with sample standard deviation \(1.1628\)) and \(\overline{Y} = 36.21\) (with sample standard deviation \(1.2038\)).

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 221 degrees of freedom.A \(t\) distribution with 480.884 degrees of freedom.A standard normal distribution.A \(t\) distribution with 578 degrees of freedom.A \(t\) distribution with 357 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0227907860

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 233 individuals on the first diet (labeled \(X\)). Further, they take a sample of 63 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 120.43\) (with sample standard deviation \(8.17\)) and \(\overline{Y} = 119.4\) (with sample standard deviation \(8.38\)).

The interest of the study is in testing whether individuals on the first diet have different average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 62 degrees of freedom.A \(t\) distribution with 96.265 degrees of freedom.A standard normal distribution.A \(t\) distribution with 232 degrees of freedom.A \(t\) distribution with 294 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0599497632

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 244 individuals from the first region (labeled \(X\)). Further, they take a sample of 421 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 176.22\) (with sample standard deviation \(6.69\)) and \(\overline{Y} = 176.31\) (with sample standard deviation \(8.47\)).

The interest of the study is in testing whether individuals from the first region are taller on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 420 degrees of freedom.A standard normal distribution.A \(t\) distribution with 603.08 degrees of freedom.A \(t\) distribution with 243 degrees of freedom.A \(t\) distribution with 663 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0101014188

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 169 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 392 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 587.02\) (with sample standard deviation \(78.69\)) and \(\overline{Y} = 598.85\) (with sample standard deviation \(70.25\)).

The interest of the study is in testing whether individuals taking the first treatment differ in their average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 288.642 degrees of freedom.A \(t\) distribution with 168 degrees of freedom.A \(t\) distribution with 559 degrees of freedom.A standard normal distribution.A \(t\) distribution with 391 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0921797286

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 331 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 113 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 122.49\) (with sample standard deviation \(7.26\)) and \(\overline{Y} = 123.57\) (with sample standard deviation \(11.3\)).

The interest of the study is in testing whether individuals taking the first medication have higher average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 442 degrees of freedom.A \(t\) distribution with 112 degrees of freedom.A \(t\) distribution with 144.814 degrees of freedom.A \(t\) distribution with 330 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0674625240

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 488 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 476 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3048.84\) (with sample standard deviation \(495.58\)) and \(\overline{Y} = 3053.3\) (with sample standard deviation \(345.9\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 962 degrees of freedom.A \(t\) distribution with 475 degrees of freedom.A standard normal distribution.A \(t\) distribution with 871.942 degrees of freedom.A \(t\) distribution with 487 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0691492492

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 237 individuals on the first diet (labeled \(X\)). Further, they take a sample of 106 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 122.3\) (with sample standard deviation \(12.76\)) and \(\overline{Y} = 124.95\) (with sample standard deviation \(7.01\)).

The interest of the study is in testing whether individuals on the first diet have lower average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 105 degrees of freedom.A \(t\) distribution with 236 degrees of freedom.A \(t\) distribution with 327.146 degrees of freedom.A \(t\) distribution with 341 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0616644128

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 482 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 308 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.75\) (with sample standard deviation \(1.3094\)) and \(\overline{Y} = 36.62\) (with sample standard deviation \(1.2016\)).

The interest of the study is in testing whether individuals taking the first medication have higher average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 788 degrees of freedom.A \(t\) distribution with 694.459 degrees of freedom.A standard normal distribution.A \(t\) distribution with 307 degrees of freedom.A \(t\) distribution with 481 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0913313011

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 440 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 90 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 713.21\) (with sample standard deviation \(80.51\)) and \(\overline{Y} = 724.32\) (with sample standard deviation \(62.67\)).

The interest of the study is in testing whether individuals taking the first treatment differ in their average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 439 degrees of freedom.A \(t\) distribution with 155.635 degrees of freedom.A \(t\) distribution with 89 degrees of freedom.A \(t\) distribution with 528 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0328647829

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 115 individuals on the first diet (labeled \(X\)). Further, they take a sample of 272 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 153.57\) (with sample standard deviation \(24.34\)) and \(\overline{Y} = 147.31\) (with sample standard deviation \(47.31\)).

The interest of the study is in testing whether individuals on the first diet have higher average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 114 degrees of freedom.A standard normal distribution.A \(t\) distribution with 370.932 degrees of freedom.A \(t\) distribution with 271 degrees of freedom.A \(t\) distribution with 385 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0922505346

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 349 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 176 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 35.6\) (with sample standard deviation \(1.2357\)) and \(\overline{Y} = 35.61\) (with sample standard deviation \(1.0113\)).

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 523 degrees of freedom.A \(t\) distribution with 348 degrees of freedom.A \(t\) distribution with 418.443 degrees of freedom.A \(t\) distribution with 175 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0238191928

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 55 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 291 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 35.33\) (with sample standard deviation \(0.949\)) and \(\overline{Y} = 35.25\) (with sample standard deviation \(1.1917\)).

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 54 degrees of freedom.A \(t\) distribution with 290 degrees of freedom.A \(t\) distribution with 344 degrees of freedom.A standard normal distribution.A \(t\) distribution with 89.504 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0682350047

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 369 individuals in the first population (labeled \(X\)). Further, they take a sample of 466 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 6.13\) (with sample standard deviation \(0.3342\)) and \(\overline{Y} = 6.13\) (with sample standard deviation \(0.5296\)).

The interest of the study is in testing whether individuals in the first population have higher average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 795.938 degrees of freedom.A \(t\) distribution with 465 degrees of freedom.A \(t\) distribution with 368 degrees of freedom.A \(t\) distribution with 833 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0725771319

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 374 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 162 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 325.52\) (with sample standard deviation \(68.1\)) and \(\overline{Y} = 319.92\) (with sample standard deviation \(31.56\)).

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 161 degrees of freedom.A \(t\) distribution with 534 degrees of freedom.A \(t\) distribution with 531.731 degrees of freedom.A standard normal distribution.A \(t\) distribution with 373 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0308354494

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 145 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 355 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3625.66\) (with sample standard deviation \(253.46\)) and \(\overline{Y} = 3685.79\) (with sample standard deviation \(760.15\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 498 degrees of freedom.A \(t\) distribution with 484.666 degrees of freedom.A \(t\) distribution with 354 degrees of freedom.A \(t\) distribution with 144 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0980653850

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 187 individuals on the first diet (labeled \(X\)). Further, they take a sample of 206 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 187.16\) (with sample standard deviation \(18.25\)) and \(\overline{Y} = 187.16\) (with sample standard deviation \(37.64\)).

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 186 degrees of freedom.A \(t\) distribution with 391 degrees of freedom.A standard normal distribution.A \(t\) distribution with 205 degrees of freedom.A \(t\) distribution with 302.562 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0398542150

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 153 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 220 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 45.92\) (with sample standard deviation \(11.95\)) and \(\overline{Y} = 47.75\) (with sample standard deviation \(5.19\)).

The interest of the study is in testing whether students in Introductory Probability study for different lengths of time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 192.199 degrees of freedom.A \(t\) distribution with 152 degrees of freedom.A \(t\) distribution with 371 degrees of freedom.A \(t\) distribution with 219 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0076688579

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 375 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 64 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3262.43\) (with sample standard deviation \(553.45\)) and \(\overline{Y} = 3239.36\) (with sample standard deviation \(721.65\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 63 degrees of freedom.A standard normal distribution.A \(t\) distribution with 437 degrees of freedom.A \(t\) distribution with 76.154 degrees of freedom.A \(t\) distribution with 374 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0156417258

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 260 individuals on the first diet (labeled \(X\)). Further, they take a sample of 262 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 114.78\) (with sample standard deviation \(10.16\)) and \(\overline{Y} = 114.4\) (with sample standard deviation \(10.94\)).

The interest of the study is in testing whether individuals on the first diet have higher average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 520 degrees of freedom.A \(t\) distribution with 259 degrees of freedom.A \(t\) distribution with 517.733 degrees of freedom.A \(t\) distribution with 261 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0822078593

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 351 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 113 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 8200\) (with sample standard deviation \(305.89\)) and \(\overline{Y} = 8187.25\) (with sample standard deviation \(391.4\)).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 350 degrees of freedom.A \(t\) distribution with 112 degrees of freedom.A \(t\) distribution with 462 degrees of freedom.A \(t\) distribution with 158.417 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0534615895

A group of researchers are studying the heights of individuals from two different regions. They collect a sample of 311 individuals from the first region (labeled \(X\)). Further, they take a sample of 311 individuals from the second region (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 172.22\) (with sample standard deviation \(8.51\)) and \(\overline{Y} = 172.07\) (with sample standard deviation \(9.49\)).

The interest of the study is in testing whether individuals from the first region are shorter on average (compared to individuals from the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 310 degrees of freedom.A \(t\) distribution with 310 degrees of freedom.A standard normal distribution.A \(t\) distribution with 612.777 degrees of freedom.A \(t\) distribution with 620 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0565614509

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 488 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 358 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3100.63\) (with sample standard deviation \(374.16\)) and \(\overline{Y} = 3140\) (with sample standard deviation \(303.83\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 357 degrees of freedom.A \(t\) distribution with 835.314 degrees of freedom.A standard normal distribution.A \(t\) distribution with 487 degrees of freedom.A \(t\) distribution with 844 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0184052073

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 158 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 311 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3135.93\) (with sample standard deviation \(320.13\)) and \(\overline{Y} = 3050.55\) (with sample standard deviation \(629.02\)).

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 310 degrees of freedom.A \(t\) distribution with 157 degrees of freedom.A \(t\) distribution with 466.995 degrees of freedom.A \(t\) distribution with 467 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0890864405

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 290 individuals in the first population (labeled \(X\)). Further, they take a sample of 176 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 4.99\) (with sample standard deviation \(0.4082\)) and \(\overline{Y} = 5.02\) (with sample standard deviation \(0.2893\)).

The interest of the study is in testing whether individuals in the first population differ in their average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 175 degrees of freedom.A \(t\) distribution with 452.954 degrees of freedom.A \(t\) distribution with 464 degrees of freedom.A \(t\) distribution with 289 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0979920831

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 242 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 470 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 10083\) (with sample standard deviation \(284.77\)) and \(\overline{Y} = 10056.94\) (with sample standard deviation \(326.48\)).

The interest of the study is in testing whether lightbulbs of the first model last longer on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 548.494 degrees of freedom.A \(t\) distribution with 710 degrees of freedom.A \(t\) distribution with 469 degrees of freedom.A standard normal distribution.A \(t\) distribution with 241 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0733618110

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 479 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 40 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3715\) (with sample standard deviation \(165.15\)) and \(\overline{Y} = 3731.29\) (with sample standard deviation \(184.77\)).

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 39 degrees of freedom.A \(t\) distribution with 517 degrees of freedom.A \(t\) distribution with 44.361 degrees of freedom.A \(t\) distribution with 478 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0269926509

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 465 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 117 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 124.96\) (with sample standard deviation \(12.01\)) and \(\overline{Y} = 127.51\) (with sample standard deviation \(10.21\)).

The interest of the study is in testing whether individuals taking the first medication have different average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 464 degrees of freedom.A \(t\) distribution with 204.63 degrees of freedom.A standard normal distribution.A \(t\) distribution with 116 degrees of freedom.A \(t\) distribution with 580 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0283991807

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 475 individuals on the first diet (labeled \(X\)). Further, they take a sample of 269 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 175.51\) (with sample standard deviation \(27.51\)) and \(\overline{Y} = 176.26\) (with sample standard deviation \(31.42\)).

The interest of the study is in testing whether individuals on the first diet have different average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 268 degrees of freedom.A \(t\) distribution with 498.127 degrees of freedom.A \(t\) distribution with 742 degrees of freedom.A \(t\) distribution with 474 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0805543176

Self Assessment 16.3

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 90 is taken, observing a sample mean of 88.5 and a standard deviation of 4.54. From the second population, a sample of size 57 is taken, observing a sample mean of 57.36 and a standard deviation of 5.46. There is a desire to determine whether \(0.93\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.18.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0236519353

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 42 is taken, observing a sample mean of 5.63 and a standard deviation of 2.2. From the second population, a sample of size 74 is taken, observing a sample mean of -46.92 and a standard deviation of 1.69. There is a desire to determine whether \(0.99\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0989948076

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 86 is taken, observing a sample mean of 53.63 and a standard deviation of 8.32. From the second population, a sample of size 17 is taken, observing a sample mean of -70.89 and a standard deviation of 6.08. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.14.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0787219446

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 89 is taken, observing a sample mean of -5.17 and a standard deviation of 7.82. From the second population, a sample of size 22 is taken, observing a sample mean of -1.82 and a standard deviation of 4.51. There is a desire to determine whether \(0.51\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.14.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0939031704

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 30 is taken, observing a sample mean of -72.51 and a standard deviation of 7.54. From the second population, a sample of size 40 is taken, observing a sample mean of 77.03 and a standard deviation of 7.1. There is a desire to determine whether \(0.63\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.19.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0657972965

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 54 is taken, observing a sample mean of -96 and a standard deviation of 1.68. From the second population, a sample of size 43 is taken, observing a sample mean of -21.91 and a standard deviation of 1.64. There is a desire to determine whether \(1.8\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0154889082

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 44 is taken, observing a sample mean of 48.79 and a standard deviation of 6.15. From the second population, a sample of size 17 is taken, observing a sample mean of -12.14 and a standard deviation of 2.95. There is a desire to determine whether \(0.74\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.19.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0872870070

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 22 is taken, observing a sample mean of -16.31 and a standard deviation of 8.04. From the second population, a sample of size 51 is taken, observing a sample mean of -33.56 and a standard deviation of 15.36. There is a desire to determine whether \(1.64\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.06.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0885027667

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 84 is taken, observing a sample mean of -76.24 and a standard deviation of 6.48. From the second population, a sample of size 43 is taken, observing a sample mean of 73.2 and a standard deviation of 4.73. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.06.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0526282693

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 90 is taken, observing a sample mean of 57.31 and a standard deviation of 6.28. From the second population, a sample of size 51 is taken, observing a sample mean of -89.08 and a standard deviation of 5.24. There is a desire to determine whether \(0.73\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.17.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0858912192

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 12 is taken, observing a sample mean of 61.28 and a standard deviation of 4.63. From the second population, a sample of size 27 is taken, observing a sample mean of 76.84 and a standard deviation of 3.22. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.06.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0937849461

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 47 is taken, observing a sample mean of 22.33 and a standard deviation of 9.88. From the second population, a sample of size 28 is taken, observing a sample mean of 65.62 and a standard deviation of 9.74. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.18.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0809193526

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 94 is taken, observing a sample mean of 67.48 and a standard deviation of 4.7. From the second population, a sample of size 86 is taken, observing a sample mean of 14.88 and a standard deviation of 5.55. There is a desire to determine whether \(\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.14.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0684161040

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 77 is taken, observing a sample mean of 3.36 and a standard deviation of 6.44. From the second population, a sample of size 31 is taken, observing a sample mean of 22.56 and a standard deviation of 7.01. There is a desire to determine whether \(\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.19.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0509451595

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 85 is taken, observing a sample mean of -25.99 and a standard deviation of 1.32. From the second population, a sample of size 64 is taken, observing a sample mean of 78.14 and a standard deviation of 1.23. There is a desire to determine whether \(\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.12.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0506622225

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 74 is taken, observing a sample mean of -73.09 and a standard deviation of 3.08. From the second population, a sample of size 35 is taken, observing a sample mean of 7.22 and a standard deviation of 2.72. There is a desire to determine whether \(0.85\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.04.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0648232291

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 23 is taken, observing a sample mean of 41.25 and a standard deviation of 4.83. From the second population, a sample of size 13 is taken, observing a sample mean of -88.65 and a standard deviation of 3.51. There is a desire to determine whether \(0.68\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.07.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0417352277

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 31 is taken, observing a sample mean of 19.47 and a standard deviation of 3.07. From the second population, a sample of size 55 is taken, observing a sample mean of 29.49 and a standard deviation of 2.21. There is a desire to determine whether \(0.66\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.16.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0062416581

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 83 is taken, observing a sample mean of -75.24 and a standard deviation of 2.33. From the second population, a sample of size 61 is taken, observing a sample mean of -26.33 and a standard deviation of 1.7. There is a desire to determine whether \(\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.03.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0301679330

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 68 is taken, observing a sample mean of -39.81 and a standard deviation of 2.43. From the second population, a sample of size 89 is taken, observing a sample mean of 40.24 and a standard deviation of 3.3. There is a desire to determine whether \(2.13\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0915272527

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 57 is taken, observing a sample mean of -39.29 and a standard deviation of 2.06. From the second population, a sample of size 34 is taken, observing a sample mean of -65.66 and a standard deviation of 3.11. There is a desire to determine whether \(2.51\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.15.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0598535873

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 10 is taken, observing a sample mean of 11.99 and a standard deviation of 1.11. From the second population, a sample of size 41 is taken, observing a sample mean of -42.4 and a standard deviation of 1.43. There is a desire to determine whether \(0.74\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.04.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0660242948

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 45 is taken, observing a sample mean of -6.76 and a standard deviation of 8.58. From the second population, a sample of size 95 is taken, observing a sample mean of -83.34 and a standard deviation of 11.29. There is a desire to determine whether \(2.16\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.18.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0443862976

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 91 is taken, observing a sample mean of -57.28 and a standard deviation of 2.26. From the second population, a sample of size 52 is taken, observing a sample mean of -35.84 and a standard deviation of 3.87. There is a desire to determine whether \(1.72\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.11.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0230172678

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 34 is taken, observing a sample mean of -73.33 and a standard deviation of 1.43. From the second population, a sample of size 86 is taken, observing a sample mean of -41.64 and a standard deviation of 1.81. There is a desire to determine whether \(1.74\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.04.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0925956106

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 12 is taken, observing a sample mean of -52.09 and a standard deviation of 1.55. From the second population, a sample of size 58 is taken, observing a sample mean of -64.17 and a standard deviation of 1.41. There is a desire to determine whether \(\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.16.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0443832842

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 41 is taken, observing a sample mean of 44.14 and a standard deviation of 3.13. From the second population, a sample of size 22 is taken, observing a sample mean of 59.68 and a standard deviation of 4.34. There is a desire to determine whether \(1.76\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.15.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0138460537

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 88 is taken, observing a sample mean of 4.92 and a standard deviation of 8.9. From the second population, a sample of size 84 is taken, observing a sample mean of 43.78 and a standard deviation of 8.29. There is a desire to determine whether \(0.66\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.12.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0296287750

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 55 is taken, observing a sample mean of 5.39 and a standard deviation of 3.3. From the second population, a sample of size 20 is taken, observing a sample mean of 18.54 and a standard deviation of 2.36. There is a desire to determine whether \(0.79\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.1.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0446797630

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 51 is taken, observing a sample mean of -93.25 and a standard deviation of 7.41. From the second population, a sample of size 83 is taken, observing a sample mean of 48.48 and a standard deviation of 12.67. There is a desire to determine whether \(1.94\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.13.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0776271150

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 25 is taken, observing a sample mean of -12.85 and a standard deviation of 9.79. From the second population, a sample of size 29 is taken, observing a sample mean of -14.81 and a standard deviation of 12.43. There is a desire to determine whether \(1.66\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.06.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0561479276

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 82 is taken, observing a sample mean of 89.35 and a standard deviation of 4.2. From the second population, a sample of size 13 is taken, observing a sample mean of 33.32 and a standard deviation of 5.1. There is a desire to determine whether \(0.77\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.05.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0141549674

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 79 is taken, observing a sample mean of -50.16 and a standard deviation of 6.85. From the second population, a sample of size 61 is taken, observing a sample mean of 96.1 and a standard deviation of 8.26. There is a desire to determine whether \(\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.16.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0626901763

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 90 is taken, observing a sample mean of 80.57 and a standard deviation of 5.73. From the second population, a sample of size 89 is taken, observing a sample mean of 86.22 and a standard deviation of 5.12. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.17.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0379700046

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 90 is taken, observing a sample mean of -66.76 and a standard deviation of 1.67. From the second population, a sample of size 28 is taken, observing a sample mean of -85.03 and a standard deviation of 1.98. There is a desire to determine whether \(0.75\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.03.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0542360376

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 85 is taken, observing a sample mean of 16.61 and a standard deviation of 3.93. From the second population, a sample of size 30 is taken, observing a sample mean of 8.58 and a standard deviation of 3.71. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.15.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0301948570

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 78 is taken, observing a sample mean of 61.71 and a standard deviation of 9.42. From the second population, a sample of size 70 is taken, observing a sample mean of 23.08 and a standard deviation of 13.45. There is a desire to determine whether \(2.93\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.07.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0125854969

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 78 is taken, observing a sample mean of 77.83 and a standard deviation of 8.06. From the second population, a sample of size 58 is taken, observing a sample mean of 51.24 and a standard deviation of 12.99. There is a desire to determine whether \(2.74\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.17.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0053274114

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 42 is taken, observing a sample mean of 52.04 and a standard deviation of 2.67. From the second population, a sample of size 89 is taken, observing a sample mean of -78.64 and a standard deviation of 3.38. There is a desire to determine whether \(1.77\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.16.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0114304456

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 21 is taken, observing a sample mean of 88.95 and a standard deviation of 4.53. From the second population, a sample of size 71 is taken, observing a sample mean of 96.01 and a standard deviation of 5.36. There is a desire to determine whether \(\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.18.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0985804140

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 68 is taken, observing a sample mean of -91.78 and a standard deviation of 6.69. From the second population, a sample of size 43 is taken, observing a sample mean of 88.77 and a standard deviation of 7.88. There is a desire to determine whether \(\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.13.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0787122181

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 19 is taken, observing a sample mean of 84.18 and a standard deviation of 2.19. From the second population, a sample of size 19 is taken, observing a sample mean of -67.5 and a standard deviation of 1.53. There is a desire to determine whether \(0.66\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.14.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0832109839

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 79 is taken, observing a sample mean of 95.08 and a standard deviation of 8.8. From the second population, a sample of size 14 is taken, observing a sample mean of -91.49 and a standard deviation of 11.08. There is a desire to determine whether \(0.66\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.14.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0988059962

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 19 is taken, observing a sample mean of -24.76 and a standard deviation of 2.69. From the second population, a sample of size 50 is taken, observing a sample mean of -23.07 and a standard deviation of 6.65. There is a desire to determine whether \(2.11\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.08.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0430470854

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 20 is taken, observing a sample mean of -5.63 and a standard deviation of 8.79. From the second population, a sample of size 24 is taken, observing a sample mean of -11.82 and a standard deviation of 7.22. There is a desire to determine whether \(0.57\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.16.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0941194476

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 20 is taken, observing a sample mean of -31.56 and a standard deviation of 2.22. From the second population, a sample of size 53 is taken, observing a sample mean of -89.08 and a standard deviation of 1.38. There is a desire to determine whether \(0.56\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.06.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0316705930

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 66 is taken, observing a sample mean of 95.58 and a standard deviation of 8.38. From the second population, a sample of size 54 is taken, observing a sample mean of -90.91 and a standard deviation of 8.6. There is a desire to determine whether \(1.36\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.18.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0308047817

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 54 is taken, observing a sample mean of 80.5 and a standard deviation of 5.58. From the second population, a sample of size 45 is taken, observing a sample mean of -51.98 and a standard deviation of 7.5. There is a desire to determine whether \(1.27\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.01.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0353941851

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 92 is taken, observing a sample mean of 89.7 and a standard deviation of 8.94. From the second population, a sample of size 84 is taken, observing a sample mean of -18.94 and a standard deviation of 7.38. There is a desire to determine whether \(0.91\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.06.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0415137728

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 11 is taken, observing a sample mean of -98.16 and a standard deviation of 7.25. From the second population, a sample of size 45 is taken, observing a sample mean of -61.5 and a standard deviation of 7.87. There is a desire to determine whether \(0.59\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.17.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0144511977

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 55 is taken, observing a sample mean of -56.21 and a standard deviation of 5.55. From the second population, a sample of size 74 is taken, observing a sample mean of 49.02 and a standard deviation of 5.51. There is a desire to determine whether \(0.74\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.16.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0002863091

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 63 is taken, observing a sample mean of -7.76 and a standard deviation of 3.81. From the second population, a sample of size 50 is taken, observing a sample mean of -71.2 and a standard deviation of 4.9. There is a desire to determine whether \(2.37\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0059348093

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 53 is taken, observing a sample mean of -30.98 and a standard deviation of 2.27. From the second population, a sample of size 50 is taken, observing a sample mean of 44.48 and a standard deviation of 5.18. There is a desire to determine whether \(2.38\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.01.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0115679322

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 81 is taken, observing a sample mean of 11.43 and a standard deviation of 9.09. From the second population, a sample of size 69 is taken, observing a sample mean of -26.46 and a standard deviation of 9.02. There is a desire to determine whether \(0.68\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.19.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0515249184

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 34 is taken, observing a sample mean of 90.2 and a standard deviation of 7.8. From the second population, a sample of size 98 is taken, observing a sample mean of -4.86 and a standard deviation of 12.78. There is a desire to determine whether \(1.87\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0173219615

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 51 is taken, observing a sample mean of 58.69 and a standard deviation of 2.26. From the second population, a sample of size 64 is taken, observing a sample mean of 87.19 and a standard deviation of 2.96. There is a desire to determine whether \(2.02\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.04.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0810986005

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 83 is taken, observing a sample mean of 73 and a standard deviation of 2.39. From the second population, a sample of size 21 is taken, observing a sample mean of 39.09 and a standard deviation of 2.41. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.19.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0287738118

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 70 is taken, observing a sample mean of -2.23 and a standard deviation of 6.65. From the second population, a sample of size 42 is taken, observing a sample mean of 40.87 and a standard deviation of 4.84. There is a desire to determine whether \(0.98\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.04.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0509651188

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 87 is taken, observing a sample mean of -62.79 and a standard deviation of 6.64. From the second population, a sample of size 76 is taken, observing a sample mean of -27.89 and a standard deviation of 9.31. There is a desire to determine whether \(1.97\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.05.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0094620061

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 28 is taken, observing a sample mean of -44.65 and a standard deviation of 9.08. From the second population, a sample of size 68 is taken, observing a sample mean of 31.85 and a standard deviation of 10.65. There is a desire to determine whether \(0.72\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.11.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0829991657

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 76 is taken, observing a sample mean of 55.42 and a standard deviation of 6.73. From the second population, a sample of size 12 is taken, observing a sample mean of -81.66 and a standard deviation of 12.78. There is a desire to determine whether \(1.75\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.07.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0027667279

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 86 is taken, observing a sample mean of 26.82 and a standard deviation of 7.79. From the second population, a sample of size 47 is taken, observing a sample mean of 20.35 and a standard deviation of 15.82. There is a desire to determine whether \(2.53\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.11.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0941529936

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 30 is taken, observing a sample mean of -89.04 and a standard deviation of 1.33. From the second population, a sample of size 94 is taken, observing a sample mean of -37.03 and a standard deviation of 1.58. There is a desire to determine whether \(2.07\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.1.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0225931888

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 92 is taken, observing a sample mean of 62.68 and a standard deviation of 1.54. From the second population, a sample of size 33 is taken, observing a sample mean of -13.55 and a standard deviation of 1.85. There is a desire to determine whether \(1.86\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.15.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0478402674

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 54 is taken, observing a sample mean of -51.85 and a standard deviation of 3.25. From the second population, a sample of size 32 is taken, observing a sample mean of -79.63 and a standard deviation of 3.52. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.19.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0555881211

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 43 is taken, observing a sample mean of -49.05 and a standard deviation of 8.48. From the second population, a sample of size 77 is taken, observing a sample mean of 64.75 and a standard deviation of 10.21. There is a desire to determine whether \(\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.2.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0210498349

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 14 is taken, observing a sample mean of -18.99 and a standard deviation of 7.96. From the second population, a sample of size 62 is taken, observing a sample mean of -88.77 and a standard deviation of 5.46. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.01.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0224868670

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 85 is taken, observing a sample mean of 54.63 and a standard deviation of 7.93. From the second population, a sample of size 74 is taken, observing a sample mean of 13.34 and a standard deviation of 5.88. There is a desire to determine whether \(0.61\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.07.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0518379818

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 45 is taken, observing a sample mean of 57.35 and a standard deviation of 2.64. From the second population, a sample of size 80 is taken, observing a sample mean of -48.85 and a standard deviation of 4.93. There is a desire to determine whether \(2.05\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0211561632

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 59 is taken, observing a sample mean of -92.33 and a standard deviation of 9.15. From the second population, a sample of size 75 is taken, observing a sample mean of -29.99 and a standard deviation of 7.83. There is a desire to determine whether \(0.61\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0716526473

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 76 is taken, observing a sample mean of 35.82 and a standard deviation of 4.59. From the second population, a sample of size 50 is taken, observing a sample mean of -77.55 and a standard deviation of 3.3. There is a desire to determine whether \(0.64\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.13.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0424225276

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 86 is taken, observing a sample mean of 51.68 and a standard deviation of 2.64. From the second population, a sample of size 76 is taken, observing a sample mean of 4.54 and a standard deviation of 2.97. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.17.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0042442636

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 14 is taken, observing a sample mean of -42.16 and a standard deviation of 6.88. From the second population, a sample of size 100 is taken, observing a sample mean of 0.51 and a standard deviation of 6.24. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0883872045

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 76 is taken, observing a sample mean of -31.3 and a standard deviation of 3.86. From the second population, a sample of size 89 is taken, observing a sample mean of 66.77 and a standard deviation of 4.68. There is a desire to determine whether \(\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.05.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0791012987

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 55 is taken, observing a sample mean of 0.49 and a standard deviation of 8.54. From the second population, a sample of size 17 is taken, observing a sample mean of -25.1 and a standard deviation of 7.7. There is a desire to determine whether \(0.96\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.06.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0088602592

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 45 is taken, observing a sample mean of -11.24 and a standard deviation of 2.46. From the second population, a sample of size 74 is taken, observing a sample mean of 28.8 and a standard deviation of 2.55. There is a desire to determine whether \(0.93\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.07.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0854480067

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 64 is taken, observing a sample mean of -4.21 and a standard deviation of 3.85. From the second population, a sample of size 82 is taken, observing a sample mean of 48.6 and a standard deviation of 4.89. There is a desire to determine whether \(2.27\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.17.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0544507052

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 43 is taken, observing a sample mean of 48.16 and a standard deviation of 6.43. From the second population, a sample of size 29 is taken, observing a sample mean of -67.68 and a standard deviation of 10.09. There is a desire to determine whether \(\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.01.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0318836634

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 50 is taken, observing a sample mean of 97.66 and a standard deviation of 8.25. From the second population, a sample of size 12 is taken, observing a sample mean of 30.1 and a standard deviation of 4.95. There is a desire to determine whether \(1.45\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.14.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0512020091

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 69 is taken, observing a sample mean of 21.24 and a standard deviation of 4.21. From the second population, a sample of size 88 is taken, observing a sample mean of -30.13 and a standard deviation of 2.95. There is a desire to determine whether \(0.92\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.07.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0534895481

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 39 is taken, observing a sample mean of -19.45 and a standard deviation of 8.32. From the second population, a sample of size 92 is taken, observing a sample mean of 10.04 and a standard deviation of 8.27. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.05.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0909111978

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 100 is taken, observing a sample mean of 39.77 and a standard deviation of 6.34. From the second population, a sample of size 32 is taken, observing a sample mean of 47.49 and a standard deviation of 6.6. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.19.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0840755492

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 85 is taken, observing a sample mean of 22.2 and a standard deviation of 7.28. From the second population, a sample of size 64 is taken, observing a sample mean of -39.83 and a standard deviation of 10.12. There is a desire to determine whether \(2.06\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.15.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0309855423

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 12 is taken, observing a sample mean of -79.29 and a standard deviation of 4.86. From the second population, a sample of size 26 is taken, observing a sample mean of -25.53 and a standard deviation of 5.44. There is a desire to determine whether \(2.27\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.17.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0487032201

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 46 is taken, observing a sample mean of 10.39 and a standard deviation of 8.93. From the second population, a sample of size 41 is taken, observing a sample mean of -8.31 and a standard deviation of 5.65. There is a desire to determine whether \(0.85\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.04.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0124437204

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 48 is taken, observing a sample mean of 76.29 and a standard deviation of 9.02. From the second population, a sample of size 74 is taken, observing a sample mean of 16.42 and a standard deviation of 13.88. There is a desire to determine whether \(1.33\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.03.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0483813826

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 77 is taken, observing a sample mean of 88.44 and a standard deviation of 2.33. From the second population, a sample of size 63 is taken, observing a sample mean of -96 and a standard deviation of 2.53. There is a desire to determine whether \(\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.12.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0693357561

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 90 is taken, observing a sample mean of -8.48 and a standard deviation of 7.85. From the second population, a sample of size 98 is taken, observing a sample mean of 82.6 and a standard deviation of 7.09. There is a desire to determine whether \(0.91\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.11.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0896112976

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 50 is taken, observing a sample mean of -26.64 and a standard deviation of 7.81. From the second population, a sample of size 40 is taken, observing a sample mean of 31.46 and a standard deviation of 10.25. There is a desire to determine whether \(\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.16.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0687010521

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 37 is taken, observing a sample mean of -25.89 and a standard deviation of 4.7. From the second population, a sample of size 58 is taken, observing a sample mean of 85.64 and a standard deviation of 3.87. There is a desire to determine whether \(1.21\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.11.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0371492153

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 79 is taken, observing a sample mean of -40.1 and a standard deviation of 5.6. From the second population, a sample of size 28 is taken, observing a sample mean of -88.84 and a standard deviation of 3.53. There is a desire to determine whether \(0.73\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.1.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0216623419

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 94 is taken, observing a sample mean of -12.47 and a standard deviation of 1.78. From the second population, a sample of size 24 is taken, observing a sample mean of -10.77 and a standard deviation of 1.55. There is a desire to determine whether \(\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.12.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0140351904

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 26 is taken, observing a sample mean of -35.97 and a standard deviation of 8.8. From the second population, a sample of size 95 is taken, observing a sample mean of -88.71 and a standard deviation of 7. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0612300384

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 80 is taken, observing a sample mean of -56.2 and a standard deviation of 9.85. From the second population, a sample of size 82 is taken, observing a sample mean of 7.34 and a standard deviation of 8.16. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.09.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0952234420

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 26 is taken, observing a sample mean of 80.16 and a standard deviation of 6.64. From the second population, a sample of size 73 is taken, observing a sample mean of -32.01 and a standard deviation of 5.73. There is a desire to determine whether \(\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.19.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0043001765

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 77 is taken, observing a sample mean of -24.4 and a standard deviation of 4.16. From the second population, a sample of size 56 is taken, observing a sample mean of 17.61 and a standard deviation of 6.44. There is a desire to determine whether \(1.61\sigma_X^2\) is really equal to \(\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.14.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0502593430

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 99 is taken, observing a sample mean of -74.1 and a standard deviation of 5.1. From the second population, a sample of size 86 is taken, observing a sample mean of -57.78 and a standard deviation of 4.04. There is a desire to determine whether \(0.54\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.19.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0101588939

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 45 is taken, observing a sample mean of 85.71 and a standard deviation of 6.94. From the second population, a sample of size 43 is taken, observing a sample mean of 36.81 and a standard deviation of 8.76. There is a desire to determine whether \(\sigma_X^2<\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.15.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0545803753

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 52 is taken, observing a sample mean of -88.79 and a standard deviation of 3.04. From the second population, a sample of size 80 is taken, observing a sample mean of 58.66 and a standard deviation of 3.86. There is a desire to determine whether \(2.09\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.14.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0706430207

Data are collected from two independent, normally distributed populations. From the first population, a sample of size 49 is taken, observing a sample mean of 72.87 and a standard deviation of 7.64. From the second population, a sample of size 21 is taken, observing a sample mean of 53.27 and a standard deviation of 14.22. There is a desire to determine whether \(2.59\sigma_X^2>\sigma_Y^2\).

Test the corresponding hypothesis with a significance level of 0.13.

1. What is the value of the test statistic used to test this hypothesis?
2. What is the \(p\)-value resulting from this hypothesis test?
3. What is the conclusion from the hypothesis test?

Based on the results, we can reject the null hypothesis.Based on the results, we fail to reject the null hypothesis.

Question ID: 0043121810

Self Assessment 16.4

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1556 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1622 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 190\) and \(Y = 144\).

The interest of the study is in testing whether individuals living in the first region experience different rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0564385585

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1053 students from the first school board (labeled \(X\)). Further, they take a sample of 1982 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 426\) and \(Y = 760\).

The interest of the study is in testing whether students from the first school board have a lower rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0105493703

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1395 residents of the first region (labeled \(X\)). Further, they take a sample of 1019 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 798\) and \(Y = 527\).

The interest of the study is in testing whether residents of the first region have a different rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0339316754

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1775 students from the first school board (labeled \(X\)). Further, they take a sample of 1130 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1502\) and \(Y = 931\).

The interest of the study is in testing whether students from the first school board have a higher rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0921551559

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1410 male children (labeled \(X\)). Further, they take a sample of 1541 female children (labeled \(Y\)).

From their sample, they observe \(X = 106\) and \(Y = 79\).

The interest of the study is in testing whether male children are left-handed in a different proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0598786932

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1858 residents of the first country (labeled \(X\)). Further, they take a sample of 1605 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 800\) and \(Y = 660\).

The interest of the study is in testing whether residents of the first country smoke in higher proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0947377464

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1021 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1635 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 143\) and \(Y = 226\).

The interest of the study is in testing whether individuals living in the first region experience higher rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0549611620

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1424 residents of the first region (labeled \(X\)). Further, they take a sample of 1108 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 766\) and \(Y = 599\).

The interest of the study is in testing whether residents of the first region have a higher rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0681985535

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1876 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1549 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 242\) and \(Y = 239\).

The interest of the study is in testing whether individuals living in the first region experience different rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0948582253

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1370 male children (labeled \(X\)). Further, they take a sample of 1595 female children (labeled \(Y\)).

From their sample, they observe \(X = 167\) and \(Y = 157\).

The interest of the study is in testing whether male children are left-handed in a different proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0532427378

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1592 females (labeled \(X\)). Further, they take a sample of 1916 males (labeled \(Y\)).

From their sample, they observe \(X = 221\) and \(Y = 249\).

The interest of the study is in testing whether females have a higher probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0436236270

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1954 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1533 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 118\) and \(Y = 101\).

The interest of the study is in testing whether individuals living in the first region experience lower rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0325780486

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1503 students from the first school board (labeled \(X\)). Further, they take a sample of 1987 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1279\) and \(Y = 1693\).

The interest of the study is in testing whether students from the first school board have a lower rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0202727376

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1213 residents of the first country (labeled \(X\)). Further, they take a sample of 1370 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 422\) and \(Y = 507\).

The interest of the study is in testing whether residents of the first country smoke in lower proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0881696519

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1185 young people (labeled \(X\)). Further, they take a sample of 1686 older people (labeled \(Y\)).

From their sample, they observe \(X = 1046\) and \(Y = 1472\).

The interest of the study is in testing whether young people have a lower rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0216467614

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1563 females (labeled \(X\)). Further, they take a sample of 1375 males (labeled \(Y\)).

From their sample, they observe \(X = 83\) and \(Y = 51\).

The interest of the study is in testing whether females have a higher probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0579404105

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1940 females (labeled \(X\)). Further, they take a sample of 1260 males (labeled \(Y\)).

From their sample, they observe \(X = 45\) and \(Y = 35\).

The interest of the study is in testing whether females have a higher probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0931413146

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1481 students from the first school board (labeled \(X\)). Further, they take a sample of 1409 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1052\) and \(Y = 1007\).

The interest of the study is in testing whether students from the first school board have a lower rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0291643264

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1176 male children (labeled \(X\)). Further, they take a sample of 1069 female children (labeled \(Y\)).

From their sample, they observe \(X = 90\) and \(Y = 98\).

The interest of the study is in testing whether male children are left-handed in a higher proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0222359874

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1472 students from the first school board (labeled \(X\)). Further, they take a sample of 1792 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1037\) and \(Y = 1227\).

The interest of the study is in testing whether students from the first school board have a higher rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0614043126

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1725 male children (labeled \(X\)). Further, they take a sample of 1227 female children (labeled \(Y\)).

From their sample, they observe \(X = 200\) and \(Y = 165\).

The interest of the study is in testing whether male children are left-handed in a lower proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0719656631

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1266 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1711 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 79\) and \(Y = 100\).

The interest of the study is in testing whether individuals living in the first region experience higher rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0344815547

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1342 male children (labeled \(X\)). Further, they take a sample of 1190 female children (labeled \(Y\)).

From their sample, they observe \(X = 187\) and \(Y = 160\).

The interest of the study is in testing whether male children are left-handed in a lower proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0838938515

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1211 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1398 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 122\) and \(Y = 108\).

The interest of the study is in testing whether individuals living in the first region experience different rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0927117775

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1926 residents of the first country (labeled \(X\)). Further, they take a sample of 1903 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 355\) and \(Y = 363\).

The interest of the study is in testing whether residents of the first country smoke in higher proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0560500694

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1730 females (labeled \(X\)). Further, they take a sample of 1412 males (labeled \(Y\)).

From their sample, they observe \(X = 127\) and \(Y = 83\).

The interest of the study is in testing whether females have a higher probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0917092626

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1033 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1560 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 63\) and \(Y = 59\).

The interest of the study is in testing whether individuals living in the first region experience different rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0920555781

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1889 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1936 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 120\) and \(Y = 96\).

The interest of the study is in testing whether individuals living in the first region experience higher rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0347020127

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1164 females (labeled \(X\)). Further, they take a sample of 1375 males (labeled \(Y\)).

From their sample, they observe \(X = 166\) and \(Y = 174\).

The interest of the study is in testing whether females have a higher probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0710816864

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1924 students from the first school board (labeled \(X\)). Further, they take a sample of 1760 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1294\) and \(Y = 1191\).

The interest of the study is in testing whether students from the first school board have a lower rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0270530982

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1705 residents of the first region (labeled \(X\)). Further, they take a sample of 1392 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 596\) and \(Y = 457\).

The interest of the study is in testing whether residents of the first region have a higher rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0971893680

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1530 young people (labeled \(X\)). Further, they take a sample of 1849 older people (labeled \(Y\)).

From their sample, they observe \(X = 1198\) and \(Y = 1474\).

The interest of the study is in testing whether young people have a lower rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0956118871

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1781 male children (labeled \(X\)). Further, they take a sample of 1209 female children (labeled \(Y\)).

From their sample, they observe \(X = 142\) and \(Y = 106\).

The interest of the study is in testing whether male children are left-handed in a higher proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0154359756

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1873 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1573 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 177\) and \(Y = 131\).

The interest of the study is in testing whether individuals living in the first region experience different rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0665372629

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1161 students from the first school board (labeled \(X\)). Further, they take a sample of 1968 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 881\) and \(Y = 1421\).

The interest of the study is in testing whether students from the first school board have different rates of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0957183268

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1412 young people (labeled \(X\)). Further, they take a sample of 1470 older people (labeled \(Y\)).

From their sample, they observe \(X = 595\) and \(Y = 673\).

The interest of the study is in testing whether young people have a different rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0183651975

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1206 students from the first school board (labeled \(X\)). Further, they take a sample of 1443 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 914\) and \(Y = 1025\).

The interest of the study is in testing whether students from the first school board have a higher rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0085118736

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1791 young people (labeled \(X\)). Further, they take a sample of 1299 older people (labeled \(Y\)).

From their sample, they observe \(X = 647\) and \(Y = 454\).

The interest of the study is in testing whether young people have a lower rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0913194180

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1609 male children (labeled \(X\)). Further, they take a sample of 1801 female children (labeled \(Y\)).

From their sample, they observe \(X = 261\) and \(Y = 257\).

The interest of the study is in testing whether male children are left-handed in a higher proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0954511045

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1399 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1266 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 161\) and \(Y = 120\).

The interest of the study is in testing whether individuals living in the first region experience higher rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0319293506

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1479 females (labeled \(X\)). Further, they take a sample of 1576 males (labeled \(Y\)).

From their sample, they observe \(X = 154\) and \(Y = 189\).

The interest of the study is in testing whether females have a different probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0140582555

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1388 residents of the first country (labeled \(X\)). Further, they take a sample of 1285 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 213\) and \(Y = 160\).

The interest of the study is in testing whether residents of the first country smoke in higher proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0868602658

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1069 students from the first school board (labeled \(X\)). Further, they take a sample of 1652 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 674\) and \(Y = 1011\).

The interest of the study is in testing whether students from the first school board have a higher rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0523614029

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1026 females (labeled \(X\)). Further, they take a sample of 1266 males (labeled \(Y\)).

From their sample, they observe \(X = 41\) and \(Y = 49\).

The interest of the study is in testing whether females have a higher probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0986474290

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1120 residents of the first region (labeled \(X\)). Further, they take a sample of 1897 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 648\) and \(Y = 1105\).

The interest of the study is in testing whether residents of the first region have a lower rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0022369559

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1626 residents of the first country (labeled \(X\)). Further, they take a sample of 1904 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 244\) and \(Y = 301\).

The interest of the study is in testing whether residents of the first country smoke in lower proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0332109440

An organizational behaviour specialist is interested in whether the rates of job satisfaction differ between people working in human resources and those working in finance. They collect a sample of 1177 people working in human resources (labeled \(X\)). Further, they take a sample of 1087 people working in finance (labeled \(Y\)).

From their sample, they observe \(X = 624\) and \(Y = 579\).

The interest of the study is in testing whether people working in human resources report lower rates of being satisfied with their job (compared to people working in finance).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0156174899

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1315 residents of the first country (labeled \(X\)). Further, they take a sample of 1960 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 183\) and \(Y = 203\).

The interest of the study is in testing whether residents of the first country smoke in higher proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0298565165

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1651 residents of the first country (labeled \(X\)). Further, they take a sample of 1653 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 330\) and \(Y = 302\).

The interest of the study is in testing whether residents of the first country smoke in higher proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0258709422

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1419 residents of the first region (labeled \(X\)). Further, they take a sample of 1183 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 1225\) and \(Y = 1047\).

The interest of the study is in testing whether residents of the first region have a lower rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0039873988

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1237 students from the first school board (labeled \(X\)). Further, they take a sample of 1215 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 983\) and \(Y = 941\).

The interest of the study is in testing whether students from the first school board have a higher rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0299608549

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1202 residents of the first country (labeled \(X\)). Further, they take a sample of 1969 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 108\) and \(Y = 149\).

The interest of the study is in testing whether residents of the first country smoke in a different proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0364505013

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1604 young people (labeled \(X\)). Further, they take a sample of 1128 older people (labeled \(Y\)).

From their sample, they observe \(X = 574\) and \(Y = 407\).

The interest of the study is in testing whether young people have a higher rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0416872102

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1598 students from the first school board (labeled \(X\)). Further, they take a sample of 1931 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1253\) and \(Y = 1562\).

The interest of the study is in testing whether students from the first school board have a lower rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0058085099

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1203 students from the first school board (labeled \(X\)). Further, they take a sample of 1870 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 800\) and \(Y = 1301\).

The interest of the study is in testing whether students from the first school board have different rates of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0940164293

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1339 students from the first school board (labeled \(X\)). Further, they take a sample of 1936 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1132\) and \(Y = 1648\).

The interest of the study is in testing whether students from the first school board have a higher rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0725681231

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1742 male children (labeled \(X\)). Further, they take a sample of 1422 female children (labeled \(Y\)).

From their sample, they observe \(X = 159\) and \(Y = 162\).

The interest of the study is in testing whether male children are left-handed in a different proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0724950003

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1547 students from the first school board (labeled \(X\)). Further, they take a sample of 1481 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 980\) and \(Y = 980\).

The interest of the study is in testing whether students from the first school board have a lower rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0844713679

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1214 residents of the first region (labeled \(X\)). Further, they take a sample of 1988 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 861\) and \(Y = 1434\).

The interest of the study is in testing whether residents of the first region have a different rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0300993914

An organizational behaviour specialist is interested in whether the rates of job satisfaction differ between people working in human resources and those working in finance. They collect a sample of 1548 people working in human resources (labeled \(X\)). Further, they take a sample of 1699 people working in finance (labeled \(Y\)).

From their sample, they observe \(X = 1053\) and \(Y = 1123\).

The interest of the study is in testing whether people working in human resources report higher rates of being satisfied with their job (compared to people working in finance).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0862692318

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1045 young people (labeled \(X\)). Further, they take a sample of 1000 older people (labeled \(Y\)).

From their sample, they observe \(X = 670\) and \(Y = 666\).

The interest of the study is in testing whether young people have a different rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0755970156

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1528 students from the first school board (labeled \(X\)). Further, they take a sample of 1740 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1214\) and \(Y = 1400\).

The interest of the study is in testing whether students from the first school board have a lower rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0385632342

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1576 residents of the first region (labeled \(X\)). Further, they take a sample of 1984 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 1152\) and \(Y = 1407\).

The interest of the study is in testing whether residents of the first region have a higher rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0016466981

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1517 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1691 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 132\) and \(Y = 143\).

The interest of the study is in testing whether individuals living in the first region experience different rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0456890316

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1835 residents of the first country (labeled \(X\)). Further, they take a sample of 1910 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 519\) and \(Y = 512\).

The interest of the study is in testing whether residents of the first country smoke in lower proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0092575881

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1752 students from the first school board (labeled \(X\)). Further, they take a sample of 1935 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1392\) and \(Y = 1530\).

The interest of the study is in testing whether students from the first school board have a lower rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0320697778

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1816 young people (labeled \(X\)). Further, they take a sample of 1678 older people (labeled \(Y\)).

From their sample, they observe \(X = 1013\) and \(Y = 954\).

The interest of the study is in testing whether young people have a higher rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0092342994

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1260 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1047 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 140\) and \(Y = 132\).

The interest of the study is in testing whether individuals living in the first region experience lower rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0943426465

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1705 females (labeled \(X\)). Further, they take a sample of 1507 males (labeled \(Y\)).

From their sample, they observe \(X = 102\) and \(Y = 102\).

The interest of the study is in testing whether females have a lower probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0617684242

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1603 students from the first school board (labeled \(X\)). Further, they take a sample of 1682 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1303\) and \(Y = 1365\).

The interest of the study is in testing whether students from the first school board have a lower rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0194557410

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1499 residents of the first region (labeled \(X\)). Further, they take a sample of 1575 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 964\) and \(Y = 1033\).

The interest of the study is in testing whether residents of the first region have a different rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0577576303

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1651 residents of the first region (labeled \(X\)). Further, they take a sample of 1196 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 602\) and \(Y = 445\).

The interest of the study is in testing whether residents of the first region have a lower rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0896948325

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1733 residents of the first country (labeled \(X\)). Further, they take a sample of 1131 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 734\) and \(Y = 437\).

The interest of the study is in testing whether residents of the first country smoke in a different proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0250716741

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1934 young people (labeled \(X\)). Further, they take a sample of 1291 older people (labeled \(Y\)).

From their sample, they observe \(X = 1164\) and \(Y = 782\).

The interest of the study is in testing whether young people have a lower rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0835904490

A group of researchers are interested in studying the rates of smartphone ownership for students from two different schoolboards. They collect a sample of 1958 students from the first school board (labeled \(X\)). Further, they take a sample of 1276 students from the second school board (labeled \(Y\)).

From their sample, they observe \(X = 1563\) and \(Y = 1038\).

The interest of the study is in testing whether students from the first school board have a higher rate of smartphone ownership (compared to students from the second school board).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0859375186

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1141 residents of the first region (labeled \(X\)). Further, they take a sample of 1104 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 294\) and \(Y = 249\).

The interest of the study is in testing whether residents of the first region have a higher rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0224584721

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1083 residents of the first region (labeled \(X\)). Further, they take a sample of 1798 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 707\) and \(Y = 1102\).

The interest of the study is in testing whether residents of the first region have a different rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0960839454

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1175 male children (labeled \(X\)). Further, they take a sample of 1471 female children (labeled \(Y\)).

From their sample, they observe \(X = 135\) and \(Y = 158\).

The interest of the study is in testing whether male children are left-handed in a lower proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0962020540

A researcher is interested in determining whether male and female children exhibit left-hand dominance with different rates. They collect a sample of 1868 male children (labeled \(X\)). Further, they take a sample of 1272 female children (labeled \(Y\)).

From their sample, they observe \(X = 173\) and \(Y = 111\).

The interest of the study is in testing whether male children are left-handed in a higher proportion of cases (compared to female children).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0384210701

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1087 residents of the first country (labeled \(X\)). Further, they take a sample of 1603 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 308\) and \(Y = 534\).

The interest of the study is in testing whether residents of the first country smoke in lower proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0452355750

An organizational behaviour specialist is interested in whether the rates of job satisfaction differ between people working in human resources and those working in finance. They collect a sample of 1757 people working in human resources (labeled \(X\)). Further, they take a sample of 1653 people working in finance (labeled \(Y\)).

From their sample, they observe \(X = 1218\) and \(Y = 1085\).

The interest of the study is in testing whether people working in human resources report higher rates of being satisfied with their job (compared to people working in finance).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0853201491

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1854 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1598 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 257\) and \(Y = 216\).

The interest of the study is in testing whether individuals living in the first region experience different rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0410599561

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1274 young people (labeled \(X\)). Further, they take a sample of 1769 older people (labeled \(Y\)).

From their sample, they observe \(X = 792\) and \(Y = 1185\).

The interest of the study is in testing whether young people have a different rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0575339749

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1151 residents of the first country (labeled \(X\)). Further, they take a sample of 1083 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 96\) and \(Y = 117\).

The interest of the study is in testing whether residents of the first country smoke in a different proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0037262264

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1608 females (labeled \(X\)). Further, they take a sample of 1254 males (labeled \(Y\)).

From their sample, they observe \(X = 74\) and \(Y = 34\).

The interest of the study is in testing whether females have a higher probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0361485877

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1434 residents of the first region (labeled \(X\)). Further, they take a sample of 1469 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 600\) and \(Y = 570\).

The interest of the study is in testing whether residents of the first region have a higher rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0021056220

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1017 residents of the first country (labeled \(X\)). Further, they take a sample of 1776 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 306\) and \(Y = 584\).

The interest of the study is in testing whether residents of the first country smoke in lower proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0871763792

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1706 young people (labeled \(X\)). Further, they take a sample of 1875 older people (labeled \(Y\)).

From their sample, they observe \(X = 1400\) and \(Y = 1524\).

The interest of the study is in testing whether young people have a lower rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0958110899

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1381 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1743 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 181\) and \(Y = 181\).

The interest of the study is in testing whether individuals living in the first region experience different rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0595687589

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1472 females (labeled \(X\)). Further, they take a sample of 1972 males (labeled \(Y\)).

From their sample, they observe \(X = 214\) and \(Y = 305\).

The interest of the study is in testing whether females have a lower probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0972033565

Researchers are considering the proportion of individuals from two different countries who smoke cigarettes. They collect a sample of 1187 residents of the first country (labeled \(X\)). Further, they take a sample of 1812 residents of the second country (labeled \(Y\)).

From their sample, they observe \(X = 520\) and \(Y = 881\).

The interest of the study is in testing whether residents of the first country smoke in a different proportion (compared to residents of the second country).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0448328817

An organizational behaviour specialist is interested in whether the rates of job satisfaction differ between people working in human resources and those working in finance. They collect a sample of 1379 people working in human resources (labeled \(X\)). Further, they take a sample of 1776 people working in finance (labeled \(Y\)).

From their sample, they observe \(X = 707\) and \(Y = 897\).

The interest of the study is in testing whether people working in human resources report different rates of job satisfaction (compared to people working in finance).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0845468977

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1067 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1862 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 76\) and \(Y = 97\).

The interest of the study is in testing whether individuals living in the first region experience higher rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0360243288

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1751 young people (labeled \(X\)). Further, they take a sample of 1946 older people (labeled \(Y\)).

From their sample, they observe \(X = 694\) and \(Y = 703\).

The interest of the study is in testing whether young people have a higher rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0487974595

A group of researchers are interested in studying the poverty rates for two different regions. They collect a sample of 1939 individuals living in the first region (labeled \(X\)). Further, they take a sample of 1137 individuals living in the second region (labeled \(Y\)).

From their sample, they observe \(X = 190\) and \(Y = 109\).

The interest of the study is in testing whether individuals living in the first region experience lower rates of poverty (compared to individuals living in the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0206010947

A municipality is interested in determining whether residents of regions within the municipality recycle at different rates. They collect a sample of 1702 residents of the first region (labeled \(X\)). Further, they take a sample of 1116 residents of the second region (labeled \(Y\)).

From their sample, they observe \(X = 834\) and \(Y = 540\).

The interest of the study is in testing whether residents of the first region have a lower rate of recycling (compared to residents of the second region).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0953874160

An organizational behaviour specialist is interested in whether the rates of job satisfaction differ between people working in human resources and those working in finance. They collect a sample of 1892 people working in human resources (labeled \(X\)). Further, they take a sample of 1935 people working in finance (labeled \(Y\)).

From their sample, they observe \(X = 883\) and \(Y = 924\).

The interest of the study is in testing whether people working in human resources report different rates of job satisfaction (compared to people working in finance).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0722856242

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1977 females (labeled \(X\)). Further, they take a sample of 1668 males (labeled \(Y\)).

From their sample, they observe \(X = 73\) and \(Y = 80\).

The interest of the study is in testing whether females have a lower probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0131194077

A researcher is interested in determining whether there is a difference in the rates of veganism between females and males. They collect a sample of 1620 females (labeled \(X\)). Further, they take a sample of 1716 males (labeled \(Y\)).

From their sample, they observe \(X = 55\) and \(Y = 63\).

The interest of the study is in testing whether females have a higher probability of being vegan (compared to males).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X \leq p_Y\) vs. \(H_A: p_X > p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0080651355

A sociologist is studying the rates of daily social media usage, comparing younger and older people. They collect a sample of 1015 young people (labeled \(X\)). Further, they take a sample of 1767 older people (labeled \(Y\)).

From their sample, they observe \(X = 707\) and \(Y = 1263\).

The interest of the study is in testing whether young people have a different rate of daily social media usage (compared to older people).

1. What set of hypotheses should be tested in this setting?

\(H_0: p_X = p_Y\) vs. \(H_A: p_X \neq p_Y\)\(H_0: p_X > p_Y\) vs. \(H_A: p_X \leq p_Y\)\(H_0: p_X \geq p_Y\) vs. \(H_A: p_X < p_Y\)\(H_0: p_X < p_Y\) vs. \(H_A: p_X \geq p_Y\)\(H_0: p_X \neq p_Y\) vs. \(H_A: p_X = p_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0110490011

Self Assessment 16.5

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 283 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 165 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3527.39\) (with sample standard deviation \(271.65\)) and \(\overline{Y} = 3609.65\) (with sample standard deviation \(585.92\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 164 degrees of freedom.A \(t\) distribution with 282 degrees of freedom.A \(t\) distribution with 205.803 degrees of freedom.A standard normal distribution.A \(t\) distribution with 446 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0525329182

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 315 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 105 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.25\) (with sample standard deviation \(0.6355\)) and \(\overline{Y} = 36.43\) (with sample standard deviation \(0.5272\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 104 degrees of freedom.A \(t\) distribution with 212.622 degrees of freedom.A \(t\) distribution with 314 degrees of freedom.A standard normal distribution.A \(t\) distribution with 418 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0358405055

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 54 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 120 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3070.85\) (with sample standard deviation \(510.22\)) and \(\overline{Y} = 3126.91\) (with sample standard deviation \(530.57\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 105.956 degrees of freedom.A standard normal distribution.A \(t\) distribution with 172 degrees of freedom.A \(t\) distribution with 119 degrees of freedom.A \(t\) distribution with 53 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0890083516

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 417 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 456 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 7074\) (with sample standard deviation \(305.19\)) and \(\overline{Y} = 7067.93\) (with sample standard deviation \(318.36\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 869.057 degrees of freedom.A \(t\) distribution with 455 degrees of freedom.A \(t\) distribution with 416 degrees of freedom.A \(t\) distribution with 871 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0442837185

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 452 individuals on the first diet (labeled \(X\)). Further, they take a sample of 293 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 115.36\) (with sample standard deviation \(12.13\)) and \(\overline{Y} = 114.16\) (with sample standard deviation \(11.74\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have higher average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 743 degrees of freedom.A \(t\) distribution with 292 degrees of freedom.A standard normal distribution.A \(t\) distribution with 451 degrees of freedom.A \(t\) distribution with 638.119 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0286486606

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 456 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 353 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 6715\) (with sample standard deviation \(309.82\)) and \(\overline{Y} = 6725.08\) (with sample standard deviation \(217.49\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last for a different average length of time (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 807 degrees of freedom.A \(t\) distribution with 352 degrees of freedom.A \(t\) distribution with 455 degrees of freedom.A \(t\) distribution with 799.75 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0660420630

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 59 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 345 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.54\) (with sample standard deviation \(0.6757\)) and \(\overline{Y} = 33.62\) (with sample standard deviation \(1.3852\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 402 degrees of freedom.A \(t\) distribution with 344 degrees of freedom.A \(t\) distribution with 58 degrees of freedom.A standard normal distribution.A \(t\) distribution with 157.603 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0694747290

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 497 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 151 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 652.99\) (with sample standard deviation \(86.8\)) and \(\overline{Y} = 642.03\) (with sample standard deviation \(41.06\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment differ in their average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 496 degrees of freedom.A standard normal distribution.A \(t\) distribution with 150 degrees of freedom.A \(t\) distribution with 535.375 degrees of freedom.A \(t\) distribution with 646 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0695518834

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 351 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 80 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3320.94\) (with sample standard deviation \(447.5\)) and \(\overline{Y} = 3347.59\) (with sample standard deviation \(418.49\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 79 degrees of freedom.A \(t\) distribution with 429 degrees of freedom.A \(t\) distribution with 123.647 degrees of freedom.A standard normal distribution.A \(t\) distribution with 350 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0770527419

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 396 individuals in the first population (labeled \(X\)). Further, they take a sample of 100 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 6.49\) (with sample standard deviation \(0.5476\)) and \(\overline{Y} = 6.6\) (with sample standard deviation \(0.6658\)). From past research, there is good reason to suspect that the population variances for individuals in the first population and individuals in the second population are, in fact, equal.

The interest of the study is in testing whether individuals in the first population have lower average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 99 degrees of freedom.A \(t\) distribution with 395 degrees of freedom.A \(t\) distribution with 494 degrees of freedom.A standard normal distribution.A \(t\) distribution with 134.726 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0992325804

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 82 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 108 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3005.66\) (with sample standard deviation \(218.63\)) and \(\overline{Y} = 3086.84\) (with sample standard deviation \(441.32\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 81 degrees of freedom.A \(t\) distribution with 107 degrees of freedom.A standard normal distribution.A \(t\) distribution with 164.63 degrees of freedom.A \(t\) distribution with 188 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0034955512

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 189 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 69 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3767.25\) (with sample standard deviation \(527.57\)) and \(\overline{Y} = 3778.14\) (with sample standard deviation \(520.16\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 188 degrees of freedom.A \(t\) distribution with 256 degrees of freedom.A \(t\) distribution with 122.421 degrees of freedom.A \(t\) distribution with 68 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0133798841

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 202 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 140 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.31\) (with sample standard deviation \(1.1563\)) and \(\overline{Y} = 33.32\) (with sample standard deviation \(0.775\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 139 degrees of freedom.A \(t\) distribution with 340 degrees of freedom.A standard normal distribution.A \(t\) distribution with 339.66 degrees of freedom.A \(t\) distribution with 201 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0072093184

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 322 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 259 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 764.17\) (with sample standard deviation \(40.46\)) and \(\overline{Y} = 755.18\) (with sample standard deviation \(25.75\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 579 degrees of freedom.A \(t\) distribution with 551.645 degrees of freedom.A \(t\) distribution with 258 degrees of freedom.A standard normal distribution.A \(t\) distribution with 321 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0768385570

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 53 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 350 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 23.75\) (with sample standard deviation \(11.84\)) and \(\overline{Y} = 26.24\) (with sample standard deviation \(13.56\)). From past research, there is good reason to suspect that the population variances for students in Introductory Probability and students in Introductory Statistics are, in fact, equal.

The interest of the study is in testing whether students in Introductory Probability study for more time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 52 degrees of freedom.A standard normal distribution.A \(t\) distribution with 401 degrees of freedom.A \(t\) distribution with 349 degrees of freedom.A \(t\) distribution with 74.271 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0785525247

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 234 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 158 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 38.05\) (with sample standard deviation \(8.23\)) and \(\overline{Y} = 36.94\) (with sample standard deviation \(9.62\)). From past research, there is good reason to suspect that the population variances for students in Introductory Probability and students in Introductory Statistics are, in fact, equal.

The interest of the study is in testing whether students in Introductory Probability study for different lengths of time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 300.987 degrees of freedom.A standard normal distribution.A \(t\) distribution with 233 degrees of freedom.A \(t\) distribution with 157 degrees of freedom.A \(t\) distribution with 390 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0782625202

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 131 male hickory shad (labeled \(X\)). Further, they take a sample of 187 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 37.73\) (with sample standard deviation \(4.32\)) and \(\overline{Y} = 39.17\) (with sample standard deviation \(4.75\)). From past research, there is good reason to suspect that the population variances for male hickory shad and female hickory shad are, in fact, equal.

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 186 degrees of freedom.A \(t\) distribution with 316 degrees of freedom.A \(t\) distribution with 130 degrees of freedom.A standard normal distribution.A \(t\) distribution with 295.371 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0010831274

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 275 individuals in the first population (labeled \(X\)). Further, they take a sample of 497 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3.29\) (with sample standard deviation \(0.5828\)) and \(\overline{Y} = 3.37\) (with sample standard deviation \(0.5025\)). From past research, there is good reason to suspect that the population variances for individuals in the first population and individuals in the second population are, in fact, equal.

The interest of the study is in testing whether individuals in the first population have lower average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 496 degrees of freedom.A \(t\) distribution with 770 degrees of freedom.A \(t\) distribution with 499.126 degrees of freedom.A \(t\) distribution with 274 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0159738757

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 332 individuals on the first diet (labeled \(X\)). Further, they take a sample of 432 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 107.66\) (with sample standard deviation \(7.69\)) and \(\overline{Y} = 107.69\) (with sample standard deviation \(10.62\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have lower average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 759.432 degrees of freedom.A \(t\) distribution with 431 degrees of freedom.A \(t\) distribution with 762 degrees of freedom.A standard normal distribution.A \(t\) distribution with 331 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0759895220

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 457 individuals on the first diet (labeled \(X\)). Further, they take a sample of 449 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 101.39\) (with sample standard deviation \(12.08\)) and \(\overline{Y} = 102.73\) (with sample standard deviation \(7.12\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have different average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 741.164 degrees of freedom.A standard normal distribution.A \(t\) distribution with 904 degrees of freedom.A \(t\) distribution with 448 degrees of freedom.A \(t\) distribution with 456 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0573379604

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 281 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 151 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 116.64\) (with sample standard deviation \(9.1\)) and \(\overline{Y} = 116.65\) (with sample standard deviation \(12.86\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 232.562 degrees of freedom.A \(t\) distribution with 430 degrees of freedom.A \(t\) distribution with 280 degrees of freedom.A \(t\) distribution with 150 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0955554993

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 64 individuals on the first diet (labeled \(X\)). Further, they take a sample of 71 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 190.71\) (with sample standard deviation \(37.23\)) and \(\overline{Y} = 176.34\) (with sample standard deviation \(17.06\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have different average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 133 degrees of freedom.A standard normal distribution.A \(t\) distribution with 63 degrees of freedom.A \(t\) distribution with 86.322 degrees of freedom.A \(t\) distribution with 70 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0255127634

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 116 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 101 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3341.05\) (with sample standard deviation \(272.45\)) and \(\overline{Y} = 3252.34\) (with sample standard deviation \(589.96\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 100 degrees of freedom.A \(t\) distribution with 215 degrees of freedom.A \(t\) distribution with 115 degrees of freedom.A standard normal distribution.A \(t\) distribution with 136.494 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0294149791

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 209 individuals in the first population (labeled \(X\)). Further, they take a sample of 440 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 4.78\) (with sample standard deviation \(0.3547\)) and \(\overline{Y} = 4.75\) (with sample standard deviation \(0.6309\)). From past research, there is good reason to suspect that the population variances for individuals in the first population and individuals in the second population are, in fact, equal.

The interest of the study is in testing whether individuals in the first population have lower average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 629.412 degrees of freedom.A \(t\) distribution with 208 degrees of freedom.A \(t\) distribution with 647 degrees of freedom.A \(t\) distribution with 439 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0315594347

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 323 individuals on the first diet (labeled \(X\)). Further, they take a sample of 111 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 198.81\) (with sample standard deviation \(41.29\)) and \(\overline{Y} = 199.79\) (with sample standard deviation \(34.83\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have higher average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 322 degrees of freedom.A \(t\) distribution with 110 degrees of freedom.A \(t\) distribution with 224.054 degrees of freedom.A standard normal distribution.A \(t\) distribution with 432 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0712930566

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 331 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 44 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 128.22\) (with sample standard deviation \(9.58\)) and \(\overline{Y} = 124.2\) (with sample standard deviation \(7.79\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have higher average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 61.702 degrees of freedom.A \(t\) distribution with 373 degrees of freedom.A \(t\) distribution with 43 degrees of freedom.A \(t\) distribution with 330 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0185733866

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 377 individuals on the first diet (labeled \(X\)). Further, they take a sample of 488 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 100.12\) (with sample standard deviation \(12.97\)) and \(\overline{Y} = 99.45\) (with sample standard deviation \(9.14\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have lower average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 863 degrees of freedom.A \(t\) distribution with 487 degrees of freedom.A \(t\) distribution with 646.391 degrees of freedom.A standard normal distribution.A \(t\) distribution with 376 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0416407343

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 360 male hickory shad (labeled \(X\)). Further, they take a sample of 253 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 35.72\) (with sample standard deviation \(3.78\)) and \(\overline{Y} = 34.86\) (with sample standard deviation \(4.8\)). From past research, there is good reason to suspect that the population variances for male hickory shad and female hickory shad are, in fact, equal.

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 252 degrees of freedom.A standard normal distribution.A \(t\) distribution with 611 degrees of freedom.A \(t\) distribution with 359 degrees of freedom.A \(t\) distribution with 458.405 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0617446241

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 388 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 122 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3764.58\) (with sample standard deviation \(552.23\)) and \(\overline{Y} = 3722.5\) (with sample standard deviation \(753.61\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 121 degrees of freedom.A \(t\) distribution with 163.848 degrees of freedom.A \(t\) distribution with 508 degrees of freedom.A \(t\) distribution with 387 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0735412623

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 108 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 88 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 14987\) (with sample standard deviation \(559.41\)) and \(\overline{Y} = 15171.31\) (with sample standard deviation \(747.94\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 157.74 degrees of freedom.A \(t\) distribution with 87 degrees of freedom.A \(t\) distribution with 194 degrees of freedom.A \(t\) distribution with 107 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0606084328

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 55 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 380 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3219.58\) (with sample standard deviation \(534.99\)) and \(\overline{Y} = 3272.35\) (with sample standard deviation \(319.9\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 59.711 degrees of freedom.A \(t\) distribution with 433 degrees of freedom.A \(t\) distribution with 379 degrees of freedom.A standard normal distribution.A \(t\) distribution with 54 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0348762674

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 413 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 445 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 38.08\) (with sample standard deviation \(9.83\)) and \(\overline{Y} = 36.73\) (with sample standard deviation \(11.98\)). From past research, there is good reason to suspect that the population variances for students in Introductory Probability and students in Introductory Statistics are, in fact, equal.

The interest of the study is in testing whether students in Introductory Probability study for more time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 412 degrees of freedom.A standard normal distribution.A \(t\) distribution with 444 degrees of freedom.A \(t\) distribution with 843.482 degrees of freedom.A \(t\) distribution with 856 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0884663829

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 386 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 489 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 34.04\) (with sample standard deviation \(1.139\)) and \(\overline{Y} = 33.85\) (with sample standard deviation \(1.4792\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have higher average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 872.485 degrees of freedom.A standard normal distribution.A \(t\) distribution with 873 degrees of freedom.A \(t\) distribution with 385 degrees of freedom.A \(t\) distribution with 488 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0502475687

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 463 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 382 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 4136\) (with sample standard deviation \(106.65\)) and \(\overline{Y} = 4112.85\) (with sample standard deviation \(109.73\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last longer on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 462 degrees of freedom.A \(t\) distribution with 843 degrees of freedom.A \(t\) distribution with 803.714 degrees of freedom.A standard normal distribution.A \(t\) distribution with 381 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0500330890

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 249 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 167 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 32.12\) (with sample standard deviation \(5.07\)) and \(\overline{Y} = 32.25\) (with sample standard deviation \(12.98\)). From past research, there is good reason to suspect that the population variances for students in Introductory Probability and students in Introductory Statistics are, in fact, equal.

The interest of the study is in testing whether students in Introductory Probability study for different lengths of time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 166 degrees of freedom.A \(t\) distribution with 414 degrees of freedom.A \(t\) distribution with 248 degrees of freedom.A \(t\) distribution with 200.306 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0048158587

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 86 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 230 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.14\) (with sample standard deviation \(1.105\)) and \(\overline{Y} = 36.33\) (with sample standard deviation \(0.9847\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 138.442 degrees of freedom.A \(t\) distribution with 85 degrees of freedom.A \(t\) distribution with 229 degrees of freedom.A standard normal distribution.A \(t\) distribution with 314 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0065995038

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 265 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 293 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 456.21\) (with sample standard deviation \(51.24\)) and \(\overline{Y} = 454.93\) (with sample standard deviation \(67.21\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 292 degrees of freedom.A \(t\) distribution with 264 degrees of freedom.A standard normal distribution.A \(t\) distribution with 540.844 degrees of freedom.A \(t\) distribution with 556 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0087126063

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 48 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 456 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 12059\) (with sample standard deviation \(363.85\)) and \(\overline{Y} = 11945.16\) (with sample standard deviation \(463.66\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last longer on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 455 degrees of freedom.A \(t\) distribution with 64.247 degrees of freedom.A \(t\) distribution with 502 degrees of freedom.A \(t\) distribution with 47 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0683049609

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 155 male hickory shad (labeled \(X\)). Further, they take a sample of 248 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 37.35\) (with sample standard deviation \(2.55\)) and \(\overline{Y} = 37.72\) (with sample standard deviation \(3.35\)). From past research, there is good reason to suspect that the population variances for male hickory shad and female hickory shad are, in fact, equal.

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 401 degrees of freedom.A \(t\) distribution with 247 degrees of freedom.A \(t\) distribution with 385.649 degrees of freedom.A standard normal distribution.A \(t\) distribution with 154 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0780706242

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 438 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 445 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3278.93\) (with sample standard deviation \(491.78\)) and \(\overline{Y} = 3265.92\) (with sample standard deviation \(428.52\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 444 degrees of freedom.A \(t\) distribution with 860.964 degrees of freedom.A \(t\) distribution with 881 degrees of freedom.A \(t\) distribution with 437 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0530564549

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 433 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 273 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.66\) (with sample standard deviation \(0.6918\)) and \(\overline{Y} = 33.79\) (with sample standard deviation \(1.0042\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 272 degrees of freedom.A standard normal distribution.A \(t\) distribution with 432 degrees of freedom.A \(t\) distribution with 434.629 degrees of freedom.A \(t\) distribution with 704 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0517478001

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 357 individuals on the first diet (labeled \(X\)). Further, they take a sample of 480 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 181.81\) (with sample standard deviation \(36.3\)) and \(\overline{Y} = 185.18\) (with sample standard deviation \(25.72\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 479 degrees of freedom.A \(t\) distribution with 608.438 degrees of freedom.A \(t\) distribution with 835 degrees of freedom.A \(t\) distribution with 356 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0833692737

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 408 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 43 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 7809\) (with sample standard deviation \(279.2\)) and \(\overline{Y} = 7874.49\) (with sample standard deviation \(219.92\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last for a different average length of time (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 42 degrees of freedom.A \(t\) distribution with 449 degrees of freedom.A \(t\) distribution with 57.31 degrees of freedom.A standard normal distribution.A \(t\) distribution with 407 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0374213398

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 287 individuals in the first population (labeled \(X\)). Further, they take a sample of 33 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3.09\) (with sample standard deviation \(0.4717\)) and \(\overline{Y} = 2.96\) (with sample standard deviation \(0.6719\)). From past research, there is good reason to suspect that the population variances for individuals in the first population and individuals in the second population are, in fact, equal.

The interest of the study is in testing whether individuals in the first population have higher average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 32 degrees of freedom.A \(t\) distribution with 318 degrees of freedom.A \(t\) distribution with 286 degrees of freedom.A standard normal distribution.A \(t\) distribution with 35.717 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0883945558

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 353 individuals on the first diet (labeled \(X\)). Further, they take a sample of 491 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 217.9\) (with sample standard deviation \(22.34\)) and \(\overline{Y} = 220.13\) (with sample standard deviation \(31.08\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 842 degrees of freedom.A \(t\) distribution with 490 degrees of freedom.A standard normal distribution.A \(t\) distribution with 842 degrees of freedom.A \(t\) distribution with 352 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0764533421

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 490 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 50 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3759.65\) (with sample standard deviation \(354.57\)) and \(\overline{Y} = 3710.85\) (with sample standard deviation \(589.87\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 52.673 degrees of freedom.A \(t\) distribution with 49 degrees of freedom.A \(t\) distribution with 489 degrees of freedom.A \(t\) distribution with 538 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0715131750

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 149 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 389 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 41.08\) (with sample standard deviation \(13.29\)) and \(\overline{Y} = 41.06\) (with sample standard deviation \(11.94\)). From past research, there is good reason to suspect that the population variances for students in Introductory Probability and students in Introductory Statistics are, in fact, equal.

The interest of the study is in testing whether students in Introductory Probability study for more time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 388 degrees of freedom.A \(t\) distribution with 244.737 degrees of freedom.A \(t\) distribution with 148 degrees of freedom.A standard normal distribution.A \(t\) distribution with 536 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0017436950

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 104 individuals on the first diet (labeled \(X\)). Further, they take a sample of 370 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 176.08\) (with sample standard deviation \(49.6\)) and \(\overline{Y} = 175.31\) (with sample standard deviation \(16.54\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have different average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 103 degrees of freedom.A \(t\) distribution with 109.51 degrees of freedom.A \(t\) distribution with 369 degrees of freedom.A \(t\) distribution with 472 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0104930984

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 292 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 424 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 314.28\) (with sample standard deviation \(28.11\)) and \(\overline{Y} = 317.08\) (with sample standard deviation \(43.27\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment have shorter average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 423 degrees of freedom.A \(t\) distribution with 291 degrees of freedom.A \(t\) distribution with 714 degrees of freedom.A \(t\) distribution with 711.755 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0545424052

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 360 individuals on the first diet (labeled \(X\)). Further, they take a sample of 466 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 151.68\) (with sample standard deviation \(31.51\)) and \(\overline{Y} = 150.65\) (with sample standard deviation \(30.86\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 465 degrees of freedom.A \(t\) distribution with 764.199 degrees of freedom.A \(t\) distribution with 824 degrees of freedom.A \(t\) distribution with 359 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0053048357

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 42 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 253 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3565.51\) (with sample standard deviation \(355.73\)) and \(\overline{Y} = 3409.31\) (with sample standard deviation \(486.03\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 252 degrees of freedom.A standard normal distribution.A \(t\) distribution with 293 degrees of freedom.A \(t\) distribution with 69.267 degrees of freedom.A \(t\) distribution with 41 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0506105850

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 270 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 339 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 103.41\) (with sample standard deviation \(12.23\)) and \(\overline{Y} = 103.74\) (with sample standard deviation \(7.98\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 441.921 degrees of freedom.A standard normal distribution.A \(t\) distribution with 338 degrees of freedom.A \(t\) distribution with 269 degrees of freedom.A \(t\) distribution with 607 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0798644428

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 381 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 193 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3301.57\) (with sample standard deviation \(532.02\)) and \(\overline{Y} = 3320.04\) (with sample standard deviation \(346.99\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 380 degrees of freedom.A \(t\) distribution with 572 degrees of freedom.A \(t\) distribution with 192 degrees of freedom.A standard normal distribution.A \(t\) distribution with 536.878 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0762981594

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 91 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 276 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 4886\) (with sample standard deviation \(176.95\)) and \(\overline{Y} = 4838.88\) (with sample standard deviation \(127.07\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last for a different average length of time (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 122.052 degrees of freedom.A \(t\) distribution with 90 degrees of freedom.A \(t\) distribution with 275 degrees of freedom.A standard normal distribution.A \(t\) distribution with 365 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0313519943

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 416 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 35 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 5489\) (with sample standard deviation \(268.85\)) and \(\overline{Y} = 5511.25\) (with sample standard deviation \(190.71\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last longer on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 46.215 degrees of freedom.A \(t\) distribution with 34 degrees of freedom.A \(t\) distribution with 415 degrees of freedom.A \(t\) distribution with 449 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0996893226

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 121 male hickory shad (labeled \(X\)). Further, they take a sample of 334 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 39.37\) (with sample standard deviation \(3.4\)) and \(\overline{Y} = 39.86\) (with sample standard deviation \(3.02\)). From past research, there is good reason to suspect that the population variances for male hickory shad and female hickory shad are, in fact, equal.

The interest of the study is in testing whether male hickory shad have different average lengths (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 453 degrees of freedom.A \(t\) distribution with 333 degrees of freedom.A \(t\) distribution with 120 degrees of freedom.A \(t\) distribution with 192.727 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0058013090

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 230 individuals on the first diet (labeled \(X\)). Further, they take a sample of 486 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 211.39\) (with sample standard deviation \(23.99\)) and \(\overline{Y} = 204.83\) (with sample standard deviation \(30.23\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have different average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 485 degrees of freedom.A standard normal distribution.A \(t\) distribution with 714 degrees of freedom.A \(t\) distribution with 229 degrees of freedom.A \(t\) distribution with 554.61 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0876332054

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 52 male hickory shad (labeled \(X\)). Further, they take a sample of 48 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 38.33\) (with sample standard deviation \(4.75\)) and \(\overline{Y} = 40.01\) (with sample standard deviation \(3.16\)). From past research, there is good reason to suspect that the population variances for male hickory shad and female hickory shad are, in fact, equal.

The interest of the study is in testing whether male hickory shad are shorter on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 51 degrees of freedom.A \(t\) distribution with 47 degrees of freedom.A \(t\) distribution with 98 degrees of freedom.A \(t\) distribution with 89.343 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0101848431

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 199 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 191 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3638.6\) (with sample standard deviation \(303.33\)) and \(\overline{Y} = 3525.7\) (with sample standard deviation \(785.57\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 388 degrees of freedom.A standard normal distribution.A \(t\) distribution with 243.484 degrees of freedom.A \(t\) distribution with 190 degrees of freedom.A \(t\) distribution with 198 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0637743130

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 268 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 462 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3783.33\) (with sample standard deviation \(580.31\)) and \(\overline{Y} = 3859.79\) (with sample standard deviation \(489.15\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 728 degrees of freedom.A \(t\) distribution with 461 degrees of freedom.A \(t\) distribution with 484.752 degrees of freedom.A \(t\) distribution with 267 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0110756319

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 65 male hickory shad (labeled \(X\)). Further, they take a sample of 253 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 32.93\) (with sample standard deviation \(2.03\)) and \(\overline{Y} = 32.78\) (with sample standard deviation \(2.48\)). From past research, there is good reason to suspect that the population variances for male hickory shad and female hickory shad are, in fact, equal.

The interest of the study is in testing whether male hickory shad have different average lengths (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 118.082 degrees of freedom.A \(t\) distribution with 316 degrees of freedom.A \(t\) distribution with 64 degrees of freedom.A \(t\) distribution with 252 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0638207235

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 447 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 219 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 298.88\) (with sample standard deviation \(78.65\)) and \(\overline{Y} = 297.03\) (with sample standard deviation \(51.09\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 664 degrees of freedom.A \(t\) distribution with 446 degrees of freedom.A \(t\) distribution with 218 degrees of freedom.A \(t\) distribution with 613.716 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0916553439

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 199 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 310 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.9\) (with sample standard deviation \(1.2004\)) and \(\overline{Y} = 36.89\) (with sample standard deviation \(1.0615\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have lower average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 309 degrees of freedom.A \(t\) distribution with 198 degrees of freedom.A \(t\) distribution with 384.578 degrees of freedom.A standard normal distribution.A \(t\) distribution with 507 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0621980278

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 223 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 493 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 678.96\) (with sample standard deviation \(23.7\)) and \(\overline{Y} = 686.14\) (with sample standard deviation \(89.68\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment have shorter average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 622.756 degrees of freedom.A \(t\) distribution with 492 degrees of freedom.A \(t\) distribution with 714 degrees of freedom.A \(t\) distribution with 222 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0185637180

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 288 male hickory shad (labeled \(X\)). Further, they take a sample of 39 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 40\) (with sample standard deviation \(3\)) and \(\overline{Y} = 39.02\) (with sample standard deviation \(2.6\)). From past research, there is good reason to suspect that the population variances for male hickory shad and female hickory shad are, in fact, equal.

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 52.71 degrees of freedom.A \(t\) distribution with 38 degrees of freedom.A \(t\) distribution with 325 degrees of freedom.A \(t\) distribution with 287 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0136512081

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 190 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 488 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 688.09\) (with sample standard deviation \(56.82\)) and \(\overline{Y} = 698.89\) (with sample standard deviation \(55.41\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment differ in their average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 487 degrees of freedom.A \(t\) distribution with 676 degrees of freedom.A \(t\) distribution with 189 degrees of freedom.A \(t\) distribution with 336.942 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0601107619

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 490 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 485 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 113.97\) (with sample standard deviation \(12.82\)) and \(\overline{Y} = 112.43\) (with sample standard deviation \(10.47\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have higher average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 484 degrees of freedom.A \(t\) distribution with 973 degrees of freedom.A \(t\) distribution with 939.2 degrees of freedom.A \(t\) distribution with 489 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0258419330

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 41 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 336 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3005.18\) (with sample standard deviation \(553.33\)) and \(\overline{Y} = 2925.1\) (with sample standard deviation \(745.2\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 375 degrees of freedom.A standard normal distribution.A \(t\) distribution with 335 degrees of freedom.A \(t\) distribution with 59.318 degrees of freedom.A \(t\) distribution with 40 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0690986942

A group of marine biologists wants to understand whether differences in length exist between male and female hickory shad. They collect a sample of 295 male hickory shad (labeled \(X\)). Further, they take a sample of 100 female hickory shad (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.7\) (with sample standard deviation \(4.91\)) and \(\overline{Y} = 32.62\) (with sample standard deviation \(3.42\)). From past research, there is good reason to suspect that the population variances for male hickory shad and female hickory shad are, in fact, equal.

The interest of the study is in testing whether male hickory shad are longer on average (compared to female hickory shad).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 99 degrees of freedom.A standard normal distribution.A \(t\) distribution with 393 degrees of freedom.A \(t\) distribution with 245.341 degrees of freedom.A \(t\) distribution with 294 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0030490365

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 108 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 125 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3061.95\) (with sample standard deviation \(407.85\)) and \(\overline{Y} = 3174.59\) (with sample standard deviation \(787.86\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 231 degrees of freedom.A \(t\) distribution with 107 degrees of freedom.A \(t\) distribution with 124 degrees of freedom.A \(t\) distribution with 191.5 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0781651570

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 154 individuals on the first diet (labeled \(X\)). Further, they take a sample of 266 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 211.24\) (with sample standard deviation \(40.22\)) and \(\overline{Y} = 214.07\) (with sample standard deviation \(26.22\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 418 degrees of freedom.A standard normal distribution.A \(t\) distribution with 153 degrees of freedom.A \(t\) distribution with 265 degrees of freedom.A \(t\) distribution with 229.531 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0442011431

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 48 individuals on the first diet (labeled \(X\)). Further, they take a sample of 232 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 167.98\) (with sample standard deviation \(46.63\)) and \(\overline{Y} = 167.98\) (with sample standard deviation \(30.35\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 278 degrees of freedom.A \(t\) distribution with 55.513 degrees of freedom.A standard normal distribution.A \(t\) distribution with 231 degrees of freedom.A \(t\) distribution with 47 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0837345557

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 154 individuals on the first diet (labeled \(X\)). Further, they take a sample of 443 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 170.49\) (with sample standard deviation \(36.13\)) and \(\overline{Y} = 178.43\) (with sample standard deviation \(40.25\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have different average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 294.521 degrees of freedom.A \(t\) distribution with 595 degrees of freedom.A \(t\) distribution with 153 degrees of freedom.A \(t\) distribution with 442 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0405800070

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 255 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 123 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 103.25\) (with sample standard deviation \(11.97\)) and \(\overline{Y} = 105.29\) (with sample standard deviation \(8.8\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 376 degrees of freedom.A \(t\) distribution with 316.03 degrees of freedom.A standard normal distribution.A \(t\) distribution with 122 degrees of freedom.A \(t\) distribution with 254 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0822228173

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 275 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 215 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 278.29\) (with sample standard deviation \(39.02\)) and \(\overline{Y} = 284.15\) (with sample standard deviation \(62.83\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment have shorter average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 214 degrees of freedom.A \(t\) distribution with 488 degrees of freedom.A \(t\) distribution with 338.48 degrees of freedom.A \(t\) distribution with 274 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0947766796

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 159 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 92 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 696.81\) (with sample standard deviation \(74.38\)) and \(\overline{Y} = 698.22\) (with sample standard deviation \(28.67\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment have longer average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 91 degrees of freedom.A \(t\) distribution with 223.924 degrees of freedom.A \(t\) distribution with 158 degrees of freedom.A \(t\) distribution with 249 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0647505277

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 221 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 165 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3246.67\) (with sample standard deviation \(311.42\)) and \(\overline{Y} = 3162.46\) (with sample standard deviation \(560.54\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins differ in their average weights (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 220 degrees of freedom.A \(t\) distribution with 238.841 degrees of freedom.A \(t\) distribution with 164 degrees of freedom.A \(t\) distribution with 384 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0185855224

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 199 individuals on the first diet (labeled \(X\)). Further, they take a sample of 312 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 160.69\) (with sample standard deviation \(20.82\)) and \(\overline{Y} = 160.71\) (with sample standard deviation \(17.08\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 311 degrees of freedom.A \(t\) distribution with 198 degrees of freedom.A \(t\) distribution with 362.001 degrees of freedom.A \(t\) distribution with 509 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0285424103

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 494 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 233 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 14074\) (with sample standard deviation \(375.06\)) and \(\overline{Y} = 14062.97\) (with sample standard deviation \(636.32\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 493 degrees of freedom.A \(t\) distribution with 232 degrees of freedom.A \(t\) distribution with 310.34 degrees of freedom.A \(t\) distribution with 725 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0764647963

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 397 individuals on the first diet (labeled \(X\)). Further, they take a sample of 412 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 102.31\) (with sample standard deviation \(10.85\)) and \(\overline{Y} = 102.33\) (with sample standard deviation \(11.1\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have higher average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 396 degrees of freedom.A \(t\) distribution with 806.834 degrees of freedom.A \(t\) distribution with 807 degrees of freedom.A standard normal distribution.A \(t\) distribution with 411 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0963671211

A group of researchers are studying the impact of two different medications on blood pressure. They collect a sample of 374 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 462 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 118.65\) (with sample standard deviation \(10.38\)) and \(\overline{Y} = 119.67\) (with sample standard deviation \(9.75\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have lower average systolic blood pressures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 834 degrees of freedom.A standard normal distribution.A \(t\) distribution with 775.861 degrees of freedom.A \(t\) distribution with 461 degrees of freedom.A \(t\) distribution with 373 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0425117365

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 157 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 485 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3246.9\) (with sample standard deviation \(380.57\)) and \(\overline{Y} = 3223.53\) (with sample standard deviation \(624.43\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh less on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 640 degrees of freedom.A \(t\) distribution with 156 degrees of freedom.A \(t\) distribution with 484 degrees of freedom.A \(t\) distribution with 438.933 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0330044035

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 301 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 433 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 413.05\) (with sample standard deviation \(20.42\)) and \(\overline{Y} = 420.27\) (with sample standard deviation \(71.77\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment have shorter average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 300 degrees of freedom.A standard normal distribution.A \(t\) distribution with 432 degrees of freedom.A \(t\) distribution with 732 degrees of freedom.A \(t\) distribution with 528.159 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0214223726

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 468 individuals in the first population (labeled \(X\)). Further, they take a sample of 102 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 4.57\) (with sample standard deviation \(0.5842\)) and \(\overline{Y} = 4.59\) (with sample standard deviation \(0.4196\)). From past research, there is good reason to suspect that the population variances for individuals in the first population and individuals in the second population are, in fact, equal.

The interest of the study is in testing whether individuals in the first population have lower average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 196.773 degrees of freedom.A \(t\) distribution with 467 degrees of freedom.A \(t\) distribution with 101 degrees of freedom.A standard normal distribution.A \(t\) distribution with 568 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0020553991

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 185 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 237 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3795.3\) (with sample standard deviation \(577.62\)) and \(\overline{Y} = 3710.26\) (with sample standard deviation \(669.02\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 420 degrees of freedom.A \(t\) distribution with 184 degrees of freedom.A \(t\) distribution with 236 degrees of freedom.A standard normal distribution.A \(t\) distribution with 415.713 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0060111471

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 82 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 494 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 44.37\) (with sample standard deviation \(11.5\)) and \(\overline{Y} = 47.47\) (with sample standard deviation \(12.82\)). From past research, there is good reason to suspect that the population variances for students in Introductory Probability and students in Introductory Statistics are, in fact, equal.

The interest of the study is in testing whether students in Introductory Probability study for less time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 117.047 degrees of freedom.A \(t\) distribution with 574 degrees of freedom.A \(t\) distribution with 493 degrees of freedom.A standard normal distribution.A \(t\) distribution with 81 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0650758512

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 336 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 283 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 31.97\) (with sample standard deviation \(7.27\)) and \(\overline{Y} = 31.19\) (with sample standard deviation \(10.25\)). From past research, there is good reason to suspect that the population variances for students in Introductory Probability and students in Introductory Statistics are, in fact, equal.

The interest of the study is in testing whether students in Introductory Probability study for different lengths of time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 335 degrees of freedom.A \(t\) distribution with 496.557 degrees of freedom.A standard normal distribution.A \(t\) distribution with 282 degrees of freedom.A \(t\) distribution with 617 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0713259462

Researchers are investigating the serum cholesterol levels of individuals who consume two different diets. They collect a sample of 377 individuals on the first diet (labeled \(X\)). Further, they take a sample of 43 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 210.58\) (with sample standard deviation \(37.34\)) and \(\overline{Y} = 223.54\) (with sample standard deviation \(33.58\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have lower average serum cholesterol levels (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 54.561 degrees of freedom.A \(t\) distribution with 418 degrees of freedom.A \(t\) distribution with 376 degrees of freedom.A \(t\) distribution with 42 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0503796074

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 415 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 174 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 44.62\) (with sample standard deviation \(14.01\)) and \(\overline{Y} = 42.5\) (with sample standard deviation \(12.51\)). From past research, there is good reason to suspect that the population variances for students in Introductory Probability and students in Introductory Statistics are, in fact, equal.

The interest of the study is in testing whether students in Introductory Probability study for different lengths of time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 414 degrees of freedom.A standard normal distribution.A \(t\) distribution with 173 degrees of freedom.A \(t\) distribution with 587 degrees of freedom.A \(t\) distribution with 361.062 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0836303169

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 414 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 412 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 6085\) (with sample standard deviation \(159.82\)) and \(\overline{Y} = 6110.06\) (with sample standard deviation \(282.75\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last for a different average length of time (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 824 degrees of freedom.A \(t\) distribution with 413 degrees of freedom.A \(t\) distribution with 648.646 degrees of freedom.A standard normal distribution.A \(t\) distribution with 411 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0736159219

A pyschologist is studying the reaction times of individuals who have taken two different medical treatments. They collect a sample of 95 individuals taking the first treatment (labeled \(X\)). Further, they take a sample of 172 individuals taking the second treatment (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 359.2\) (with sample standard deviation \(64.73\)) and \(\overline{Y} = 373.6\) (with sample standard deviation \(88.27\)). From past research, there is good reason to suspect that the population variances for individuals taking the first treatment and individuals taking the second treatment are, in fact, equal.

The interest of the study is in testing whether individuals taking the first treatment have shorter average reaction times (compared to individuals taking the second treatment).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 244.482 degrees of freedom.A \(t\) distribution with 94 degrees of freedom.A \(t\) distribution with 265 degrees of freedom.A \(t\) distribution with 171 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0172366852

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 387 individuals in the first population (labeled \(X\)). Further, they take a sample of 108 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 5.31\) (with sample standard deviation \(0.666\)) and \(\overline{Y} = 5.48\) (with sample standard deviation \(0.7107\)). From past research, there is good reason to suspect that the population variances for individuals in the first population and individuals in the second population are, in fact, equal.

The interest of the study is in testing whether individuals in the first population differ in their average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 386 degrees of freedom.A standard normal distribution.A \(t\) distribution with 163.155 degrees of freedom.A \(t\) distribution with 107 degrees of freedom.A \(t\) distribution with 493 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0886635357

A research nurse wants to understand how the presence (or absence) of prenatal vitamins impacts the weight of newborns. They collect a sample of 228 newborns whose mothers took prenatal viatmins (labeled \(X\)). Further, they take a sample of 312 newborns whose mothers did not take prenatal vitamins (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3119.78\) (with sample standard deviation \(569.68\)) and \(\overline{Y} = 3099.77\) (with sample standard deviation \(206.34\)). From past research, there is good reason to suspect that the population variances for newborns whose mothers took prenatal viatmins and newborns whose mothers did not take prenatal vitamins are, in fact, equal.

The interest of the study is in testing whether newborns whose mothers took prenatal viatmins weigh more on average (compared to newborns whose mothers did not take prenatal vitamins).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 270.795 degrees of freedom.A \(t\) distribution with 227 degrees of freedom.A \(t\) distribution with 538 degrees of freedom.A \(t\) distribution with 311 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0117039764

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 296 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 81 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 36.64\) (with sample standard deviation \(1.3175\)) and \(\overline{Y} = 36.49\) (with sample standard deviation \(1.1276\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 80 degrees of freedom.A \(t\) distribution with 375 degrees of freedom.A \(t\) distribution with 145.434 degrees of freedom.A standard normal distribution.A \(t\) distribution with 295 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0286355455

Researchers are studying the red blood cell counts for individuals from two different populations. They collect a sample of 122 individuals in the first population (labeled \(X\)). Further, they take a sample of 314 individuals in the second population (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3.54\) (with sample standard deviation \(0.4249\)) and \(\overline{Y} = 3.49\) (with sample standard deviation \(0.7003\)). From past research, there is good reason to suspect that the population variances for individuals in the first population and individuals in the second population are, in fact, equal.

The interest of the study is in testing whether individuals in the first population differ in their average red blood cell counts (compared to individuals in the second population).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 357.325 degrees of freedom.A \(t\) distribution with 434 degrees of freedom.A \(t\) distribution with 313 degrees of freedom.A \(t\) distribution with 121 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0840490372

Medical researchers are interested in studying how internal body temperatures are impacted by two different medications. They collect a sample of 182 individuals taking the first medication (labeled \(X\)). Further, they take a sample of 353 individuals taking the second medication (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 33.21\) (with sample standard deviation \(1.1768\)) and \(\overline{Y} = 33.3\) (with sample standard deviation \(1.4427\)). From past research, there is good reason to suspect that the population variances for individuals taking the first medication and individuals taking the second medication are, in fact, equal.

The interest of the study is in testing whether individuals taking the first medication have different average body temperatures (compared to individuals taking the second medication).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 181 degrees of freedom.A \(t\) distribution with 533 degrees of freedom.A standard normal distribution.A \(t\) distribution with 352 degrees of freedom.A \(t\) distribution with 435.676 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0906104857

A professor is interested in comparing the average number of hours that students study for Introductory Probability compared to Introductory Statistics. They collect a sample of 350 students in Introductory Probability (labeled \(X\)). Further, they take a sample of 266 students in Introductory Statistics (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 38.98\) (with sample standard deviation \(9\)) and \(\overline{Y} = 38.07\) (with sample standard deviation \(12.54\)). From past research, there is good reason to suspect that the population variances for students in Introductory Probability and students in Introductory Statistics are, in fact, equal.

The interest of the study is in testing whether students in Introductory Probability study for less time (compared to students in Introductory Statistics).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 349 degrees of freedom.A \(t\) distribution with 459.61 degrees of freedom.A standard normal distribution.A \(t\) distribution with 614 degrees of freedom.A \(t\) distribution with 265 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0224006809

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 160 individuals on the first diet (labeled \(X\)). Further, they take a sample of 349 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 123.16\) (with sample standard deviation \(9.87\)) and \(\overline{Y} = 123.68\) (with sample standard deviation \(12.87\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have higher average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 159 degrees of freedom.A \(t\) distribution with 507 degrees of freedom.A \(t\) distribution with 394.087 degrees of freedom.A standard normal distribution.A \(t\) distribution with 348 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0293283340

A medical researcher in interested in understanding the impact of two different diets on blood pressure. They collect a sample of 467 individuals on the first diet (labeled \(X\)). Further, they take a sample of 90 individuals on the second diet (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 122.97\) (with sample standard deviation \(12.83\)) and \(\overline{Y} = 122.01\) (with sample standard deviation \(9.35\)). From past research, there is good reason to suspect that the population variances for individuals on the first diet and individuals on the second diet are, in fact, equal.

The interest of the study is in testing whether individuals on the first diet have higher average systolic blood pressures (compared to individuals on the second diet).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 161.255 degrees of freedom.A standard normal distribution.A \(t\) distribution with 89 degrees of freedom.A \(t\) distribution with 555 degrees of freedom.A \(t\) distribution with 466 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0388933358

A lightbulb manufacturer wants to compare the lifespan for two different models of their lightbulbs. They collect a sample of 305 lightbulbs of the first model (labeled \(X\)). Further, they take a sample of 483 lightbulbs of the second model (labeled \(Y\)).

From their sample, they observe \(\overline{X} = 3799\) (with sample standard deviation \(188.06\)) and \(\overline{Y} = 3810.74\) (with sample standard deviation \(170.36\)). From past research, there is good reason to suspect that the population variances for lightbulbs of the first model and lightbulbs of the second model are, in fact, equal.

The interest of the study is in testing whether lightbulbs of the first model last shorter on average (compared to lightbulbs of the second model).

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 304 degrees of freedom.A \(t\) distribution with 599.213 degrees of freedom.A \(t\) distribution with 786 degrees of freedom.A \(t\) distribution with 482 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0456596001

Self Assessment 16.6

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 59 observations, they observe:

• \(\overline{X} = 0.0586\)
• \(\overline{Y} = 0.0587\)
• \(S_X = 0.006\)
• \(S_Y = 0.014\)
• \(S_{XY} = 0\)

Their interest is in whether whether the first type of tires exhibit less wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 58 degrees of freedom.A \(t\) distribution with 78.611 degrees of freedom.A \(t\) distribution with 116 degrees of freedom.A standard normal distribution.A \(t\) distribution with 59 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0231601659

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 423 observations, they observe:

• \(\overline{X} = 0.0674\)
• \(\overline{Y} = 0.066\)
• \(S_X = 0.002\)
• \(S_Y = 0.015\)
• \(S_{XY} = 0\)

Their interest is in whether whether the first type of tires exhibit more wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 423 degrees of freedom.A \(t\) distribution with 437 degrees of freedom.A \(t\) distribution with 422 degrees of freedom.A \(t\) distribution with 844 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0384185547

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 199 observations, they observe:

• \(\overline{X} = 405.63\)
• \(\overline{Y} = 402.43\)
• \(S_X = 68.78\)
• \(S_Y = 82.58\)
• \(S_{XY} = 2243.199\)

Their interest is in whether whether the stimulant decreases reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 198 degrees of freedom.A standard normal distribution.A \(t\) distribution with 383.459 degrees of freedom.A \(t\) distribution with 199 degrees of freedom.A \(t\) distribution with 396 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0584287650

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 109 observations, they observe:

• \(\overline{X} = 45.9\)
• \(\overline{Y} = 43.3\)
• \(S_X = 11.37\)
• \(S_Y = 9.22\)
• \(S_{XY} = 29.3702\)

Their interest is in whether whether the peer tutoring impacts student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 207.159 degrees of freedom.A standard normal distribution.A \(t\) distribution with 108 degrees of freedom.A \(t\) distribution with 109 degrees of freedom.A \(t\) distribution with 216 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0307534620

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 364 observations, they observe:

• \(\overline{X} = 128.63\)
• \(\overline{Y} = 127.85\)
• \(S_X = 9.16\)
• \(S_Y = 7.66\)
• \(S_{XY} = 45.8677\)

Their interest is in whether whether the diet changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 726 degrees of freedom.A \(t\) distribution with 364 degrees of freedom.A standard normal distribution.A \(t\) distribution with 363 degrees of freedom.A \(t\) distribution with 703.958 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0405365559

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 305 observations, they observe:

• \(\overline{X} = 471.37\)
• \(\overline{Y} = 482.9\)
• \(S_X = 59.21\)
• \(S_Y = 87.99\)
• \(S_{XY} = 2606.133\)

Their interest is in whether whether the stimulant increases reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 608 degrees of freedom.A \(t\) distribution with 304 degrees of freedom.A \(t\) distribution with 532.467 degrees of freedom.A \(t\) distribution with 305 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0575212160

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 49 observations, they observe:

• \(\overline{X} = 102.61\)
• \(\overline{Y} = 102.73\)
• \(S_X = 10.35\)
• \(S_Y = 11.69\)
• \(S_{XY} = 69.8181\)

Their interest is in whether whether the diet lowers patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 96 degrees of freedom.A standard normal distribution.A \(t\) distribution with 48 degrees of freedom.A \(t\) distribution with 94.611 degrees of freedom.A \(t\) distribution with 49 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0644026826

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 43 observations, they observe:

• \(\overline{X} = 7.66\)
• \(\overline{Y} = 8.66\)
• \(S_X = 2.35\)
• \(S_Y = 2.17\)
• \(S_{XY} = 1.8571\)

Their interest is in whether whether the males self-report doing less domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 83.472 degrees of freedom.A \(t\) distribution with 43 degrees of freedom.A \(t\) distribution with 42 degrees of freedom.A standard normal distribution.A \(t\) distribution with 84 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0518662551

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 60 observations, they observe:

• \(\overline{X} = 128.83\)
• \(\overline{Y} = 129.55\)
• \(S_X = 10.07\)
• \(S_Y = 8.87\)
• \(S_{XY} = 20.5382\)

Their interest is in whether whether the diet increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 60 degrees of freedom.A \(t\) distribution with 116.15 degrees of freedom.A \(t\) distribution with 59 degrees of freedom.A standard normal distribution.A \(t\) distribution with 118 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0626527704

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 176 observations, they observe:

• \(\overline{X} = 103.19\)
• \(\overline{Y} = 101.76\)
• \(S_X = 12.44\)
• \(S_Y = 8.92\)
• \(S_{XY} = 28.1639\)

Their interest is in whether whether the medication lowers patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 176 degrees of freedom.A \(t\) distribution with 350 degrees of freedom.A \(t\) distribution with 175 degrees of freedom.A \(t\) distribution with 317.328 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0440560154

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 262 observations, they observe:

• \(\overline{X} = 128.71\)
• \(\overline{Y} = 128.39\)
• \(S_X = 11.59\)
• \(S_Y = 11.46\)
• \(S_{XY} = 70.6622\)

Their interest is in whether whether the medication changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 261 degrees of freedom.A \(t\) distribution with 522 degrees of freedom.A \(t\) distribution with 521.934 degrees of freedom.A standard normal distribution.A \(t\) distribution with 262 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0789451133

A farmer hopes to understand the impact of fertilizer application on the productivity of their plots. They consider the application of fertilizer directly to rows of their fields. Within each row, they measure the unfertilized yield (\(X\)) and the fertilized yield (\(Y\)).

In a sample of 432 observations, they observe:

• \(\overline{X} = 84.56\)
• \(\overline{Y} = 84.45\)
• \(S_X = 12.77\)
• \(S_Y = 12.62\)
• \(S_{XY} = 76.2845\)

Their interest is in whether whether the fertilized rows have higher yields.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 431 degrees of freedom.A \(t\) distribution with 432 degrees of freedom.A \(t\) distribution with 861.88 degrees of freedom.A \(t\) distribution with 862 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0763549717

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 230 observations, they observe:

• \(\overline{X} = 48.5\)
• \(\overline{Y} = 49.8\)
• \(S_X = 17.61\)
• \(S_Y = 14.94\)
• \(S_{XY} = 73.9349\)

Their interest is in whether whether the peer tutoring impacts student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 446.152 degrees of freedom.A \(t\) distribution with 229 degrees of freedom.A \(t\) distribution with 230 degrees of freedom.A \(t\) distribution with 458 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0304855342

A farmer hopes to understand the impact of fertilizer application on the productivity of their plots. They consider the application of fertilizer directly to rows of their fields. Within each row, they measure the unfertilized yield (\(X\)) and the fertilized yield (\(Y\)).

In a sample of 356 observations, they observe:

• \(\overline{X} = 102.76\)
• \(\overline{Y} = 100.77\)
• \(S_X = 14.55\)
• \(S_Y = 14.51\)
• \(S_{XY} = 17.0099\)

Their interest is in whether whether the fertilizer impacts the yields of the rows.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 355 degrees of freedom.A \(t\) distribution with 709.995 degrees of freedom.A \(t\) distribution with 356 degrees of freedom.A \(t\) distribution with 710 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0023997314

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 435 observations, they observe:

• \(\overline{X} = 301.67\)
• \(\overline{Y} = 300.1\)
• \(S_X = 75.15\)
• \(S_Y = 51.77\)
• \(S_{XY} = 386.8416\)

Their interest is in whether whether the stimulant increases reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 434 degrees of freedom.A standard normal distribution.A \(t\) distribution with 868 degrees of freedom.A \(t\) distribution with 770.206 degrees of freedom.A \(t\) distribution with 435 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0657351602

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 177 observations, they observe:

• \(\overline{X} = 8.54\)
• \(\overline{Y} = 7.62\)
• \(S_X = 9.92\)
• \(S_Y = 8.57\)
• \(S_{XY} = 40.2938\)

Their interest is in whether whether the males self-report doing less domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 352 degrees of freedom.A \(t\) distribution with 176 degrees of freedom.A standard normal distribution.A \(t\) distribution with 177 degrees of freedom.A \(t\) distribution with 344.727 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0730127146

A farmer hopes to understand the impact of fertilizer application on the productivity of their plots. They consider the application of fertilizer directly to rows of their fields. Within each row, they measure the unfertilized yield (\(X\)) and the fertilized yield (\(Y\)).

In a sample of 142 observations, they observe:

• \(\overline{X} = 99.06\)
• \(\overline{Y} = 100.18\)
• \(S_X = 13.49\)
• \(S_Y = 18.44\)
• \(S_{XY} = 37.0693\)

Their interest is in whether whether the fertilizer impacts the yields of the rows.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 142 degrees of freedom.A standard normal distribution.A \(t\) distribution with 141 degrees of freedom.A \(t\) distribution with 258.319 degrees of freedom.A \(t\) distribution with 282 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0795003183

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 109 observations, they observe:

• \(\overline{X} = 105.59\)
• \(\overline{Y} = 105.1\)
• \(S_X = 7.85\)
• \(S_Y = 11.01\)
• \(S_{XY} = 35.1326\)

Their interest is in whether whether the medication changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 108 degrees of freedom.A \(t\) distribution with 195.255 degrees of freedom.A \(t\) distribution with 216 degrees of freedom.A standard normal distribution.A \(t\) distribution with 109 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0778057652

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 76 observations, they observe:

• \(\overline{X} = 119.45\)
• \(\overline{Y} = 121.92\)
• \(S_X = 11.41\)
• \(S_Y = 9.41\)
• \(S_{XY} = 30.0592\)

Their interest is in whether whether the diet increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 144.754 degrees of freedom.A standard normal distribution.A \(t\) distribution with 150 degrees of freedom.A \(t\) distribution with 76 degrees of freedom.A \(t\) distribution with 75 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0015452120

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 432 observations, they observe:

• \(\overline{X} = 0.0386\)
• \(\overline{Y} = 0.0388\)
• \(S_X = 0.013\)
• \(S_Y = 0.002\)
• \(S_{XY} = 0\)

Their interest is in whether whether the two types of tires exhibit different wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 451.391 degrees of freedom.A \(t\) distribution with 431 degrees of freedom.A standard normal distribution.A \(t\) distribution with 862 degrees of freedom.A \(t\) distribution with 432 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0378863204

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 176 observations, they observe:

• \(\overline{X} = 30.07\)
• \(\overline{Y} = 30.11\)
• \(S_X = 1.784\)
• \(S_Y = 0.23\)
• \(S_{XY} = 0.0888\)

Their interest is in whether whether the two devices report different concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 350 degrees of freedom.A \(t\) distribution with 175 degrees of freedom.A \(t\) distribution with 180.816 degrees of freedom.A \(t\) distribution with 176 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0727204690

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 290 observations, they observe:

• \(\overline{X} = 113.88\)
• \(\overline{Y} = 112.22\)
• \(S_X = 11.84\)
• \(S_Y = 9.12\)
• \(S_{XY} = 31.8607\)

Their interest is in whether whether the diet lowers patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 542.647 degrees of freedom.A \(t\) distribution with 290 degrees of freedom.A \(t\) distribution with 578 degrees of freedom.A \(t\) distribution with 289 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0367261762

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 265 observations, they observe:

• \(\overline{X} = 11.614\)
• \(\overline{Y} = 11.614\)
• \(S_X = 0.069\)
• \(S_Y = 0.061\)
• \(S_{XY} = 0.0028\)

Their interest is in whether whether the parts had smaller diameters before calibration.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 264 degrees of freedom.A \(t\) distribution with 520.18 degrees of freedom.A \(t\) distribution with 528 degrees of freedom.A \(t\) distribution with 265 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0107601454

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 481 observations, they observe:

• \(\overline{X} = 42.1\)
• \(\overline{Y} = 41.7\)
• \(S_X = 7.09\)
• \(S_Y = 16.27\)
• \(S_{XY} = 76.5228\)

Their interest is in whether whether the peer tutoring impacts student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 960 degrees of freedom.A \(t\) distribution with 480 degrees of freedom.A standard normal distribution.A \(t\) distribution with 481 degrees of freedom.A \(t\) distribution with 655.956 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0551783237

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 285 observations, they observe:

• \(\overline{X} = 4.49\)
• \(\overline{Y} = 4.46\)
• \(S_X = 8.87\)
• \(S_Y = 7.48\)
• \(S_{XY} = 18.3757\)

Their interest is in whether whether the males self-report doing more domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 552.262 degrees of freedom.A \(t\) distribution with 284 degrees of freedom.A standard normal distribution.A \(t\) distribution with 285 degrees of freedom.A \(t\) distribution with 568 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0255958544

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 304 observations, they observe:

• \(\overline{X} = 9.416\)
• \(\overline{Y} = 9.412\)
• \(S_X = 0.026\)
• \(S_Y = 0.069\)
• \(S_{XY} = 0.0007\)

Their interest is in whether whether the parts had smaller diameters before calibration.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 387.344 degrees of freedom.A \(t\) distribution with 606 degrees of freedom.A \(t\) distribution with 303 degrees of freedom.A standard normal distribution.A \(t\) distribution with 304 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0785655970

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 60 observations, they observe:

• \(\overline{X} = 8.821\)
• \(\overline{Y} = 8.808\)
• \(S_X = 0.056\)
• \(S_Y = 0.056\)
• \(S_{XY} = 0.0014\)

Their interest is in whether whether the parts were larger in diameter before calibration.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 60 degrees of freedom.A \(t\) distribution with 118 degrees of freedom.A \(t\) distribution with 118 degrees of freedom.A \(t\) distribution with 59 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0004047733

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 379 observations, they observe:

• \(\overline{X} = 20.71\)
• \(\overline{Y} = 20.68\)
• \(S_X = 1.813\)
• \(S_Y = 1.81\)
• \(S_{XY} = 1.9523\)

Their interest is in whether whether the first device reports higher concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 755.998 degrees of freedom.A standard normal distribution.A \(t\) distribution with 379 degrees of freedom.A \(t\) distribution with 756 degrees of freedom.A \(t\) distribution with 378 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0309218477

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 50 observations, they observe:

• \(\overline{X} = 20.66\)
• \(\overline{Y} = 20.29\)
• \(S_X = 0.806\)
• \(S_Y = 0.856\)
• \(S_{XY} = 0.1654\)

Their interest is in whether whether the two devices report different concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 98 degrees of freedom.A standard normal distribution.A \(t\) distribution with 49 degrees of freedom.A \(t\) distribution with 97.647 degrees of freedom.A \(t\) distribution with 50 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0463924164

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 154 observations, they observe:

• \(\overline{X} = 57.7\)
• \(\overline{Y} = 58.6\)
• \(S_X = 14.54\)
• \(S_Y = 10.59\)
• \(S_{XY} = 57.4455\)

Their interest is in whether whether the peer tutoring improves student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 154 degrees of freedom.A \(t\) distribution with 153 degrees of freedom.A \(t\) distribution with 279.677 degrees of freedom.A standard normal distribution.A \(t\) distribution with 306 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0289006566

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 369 observations, they observe:

• \(\overline{X} = 498.55\)
• \(\overline{Y} = 507.37\)
• \(S_X = 66.41\)
• \(S_Y = 63.38\)
• \(S_{XY} = 439.73\)

Their interest is in whether whether the stimulant increases reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 736 degrees of freedom.A \(t\) distribution with 368 degrees of freedom.A \(t\) distribution with 734.401 degrees of freedom.A \(t\) distribution with 369 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0751358840

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 110 observations, they observe:

• \(\overline{X} = 58.2\)
• \(\overline{Y} = 56.5\)
• \(S_X = 11.74\)
• \(S_Y = 13.59\)
• \(S_{XY} = 91.4198\)

Their interest is in whether whether the peer tutoring worsens student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 110 degrees of freedom.A \(t\) distribution with 213.493 degrees of freedom.A \(t\) distribution with 109 degrees of freedom.A \(t\) distribution with 218 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0605687075

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 194 observations, they observe:

• \(\overline{X} = 8.747\)
• \(\overline{Y} = 8.74\)
• \(S_X = 0.05\)
• \(S_Y = 0.037\)
• \(S_{XY} = 0.0011\)

Their interest is in whether whether calibration changed the diameters of the parts.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 386 degrees of freedom.A standard normal distribution.A \(t\) distribution with 194 degrees of freedom.A \(t\) distribution with 193 degrees of freedom.A \(t\) distribution with 355.612 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0588697397

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 217 observations, they observe:

• \(\overline{X} = 29.1\)
• \(\overline{Y} = 29.33\)
• \(S_X = 1.937\)
• \(S_Y = 0.896\)
• \(S_{XY} = 1.1163\)

Their interest is in whether whether the second device reports higher concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 216 degrees of freedom.A \(t\) distribution with 304.389 degrees of freedom.A \(t\) distribution with 217 degrees of freedom.A \(t\) distribution with 432 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0910060274

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 216 observations, they observe:

• \(\overline{X} = 54.9\)
• \(\overline{Y} = 53.3\)
• \(S_X = 13.41\)
• \(S_Y = 14.33\)
• \(S_{XY} = 68.7571\)

Their interest is in whether whether the peer tutoring impacts student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 215 degrees of freedom.A \(t\) distribution with 428.121 degrees of freedom.A \(t\) distribution with 216 degrees of freedom.A standard normal distribution.A \(t\) distribution with 430 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0614268916

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 190 observations, they observe:

• \(\overline{X} = 114.89\)
• \(\overline{Y} = 117.67\)
• \(S_X = 11.35\)
• \(S_Y = 7.2\)
• \(S_{XY} = 15.4103\)

Their interest is in whether whether the diet changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 190 degrees of freedom.A \(t\) distribution with 189 degrees of freedom.A \(t\) distribution with 378 degrees of freedom.A \(t\) distribution with 319.913 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0712337773

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 229 observations, they observe:

• \(\overline{X} = 103.97\)
• \(\overline{Y} = 105.46\)
• \(S_X = 10.12\)
• \(S_Y = 8.89\)
• \(S_{XY} = 8.8165\)

Their interest is in whether whether the medication increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 456 degrees of freedom.A \(t\) distribution with 228 degrees of freedom.A \(t\) distribution with 229 degrees of freedom.A \(t\) distribution with 448.551 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0934352710

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 474 observations, they observe:

• \(\overline{X} = 124.11\)
• \(\overline{Y} = 124.75\)
• \(S_X = 7.13\)
• \(S_Y = 7.71\)
• \(S_{XY} = 25.4417\)

Their interest is in whether whether the medication increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 474 degrees of freedom.A \(t\) distribution with 940.272 degrees of freedom.A \(t\) distribution with 473 degrees of freedom.A \(t\) distribution with 946 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0982661137

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 423 observations, they observe:

• \(\overline{X} = 39.56\)
• \(\overline{Y} = 39.52\)
• \(S_X = 0.424\)
• \(S_Y = 1.468\)
• \(S_{XY} = 0.3689\)

Their interest is in whether whether the two devices report different concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 423 degrees of freedom.A \(t\) distribution with 491.921 degrees of freedom.A \(t\) distribution with 422 degrees of freedom.A \(t\) distribution with 844 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0419467190

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 201 observations, they observe:

• \(\overline{X} = 288.03\)
• \(\overline{Y} = 285.92\)
• \(S_X = 79.06\)
• \(S_Y = 95.43\)
• \(S_{XY} = 2157.009\)

Their interest is in whether whether the stimulant increases reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 200 degrees of freedom.A \(t\) distribution with 400 degrees of freedom.A \(t\) distribution with 386.625 degrees of freedom.A standard normal distribution.A \(t\) distribution with 201 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.16.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0356919539

A farmer hopes to understand the impact of fertilizer application on the productivity of their plots. They consider the application of fertilizer directly to rows of their fields. Within each row, they measure the unfertilized yield (\(X\)) and the fertilized yield (\(Y\)).

In a sample of 285 observations, they observe:

• \(\overline{X} = 118.3\)
• \(\overline{Y} = 118.04\)
• \(S_X = 15.37\)
• \(S_Y = 14.74\)
• \(S_{XY} = 135.8456\)

Their interest is in whether whether the fertilizer impacts the yields of the rows.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 568 degrees of freedom.A standard normal distribution.A \(t\) distribution with 567.008 degrees of freedom.A \(t\) distribution with 284 degrees of freedom.A \(t\) distribution with 285 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.18.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0306079464

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 474 observations, they observe:

• \(\overline{X} = 124.48\)
• \(\overline{Y} = 124.58\)
• \(S_X = 11.66\)
• \(S_Y = 8.54\)
• \(S_{XY} = 4.0693\)

Their interest is in whether whether the medication changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 946 degrees of freedom.A \(t\) distribution with 867.07 degrees of freedom.A \(t\) distribution with 473 degrees of freedom.A \(t\) distribution with 474 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0997474646

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 353 observations, they observe:

• \(\overline{X} = 8.74\)
• \(\overline{Y} = 9.3\)
• \(S_X = 3.16\)
• \(S_Y = 9.42\)
• \(S_{XY} = 16.4718\)

Their interest is in whether whether the males self-report doing less domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 353 degrees of freedom.A \(t\) distribution with 704 degrees of freedom.A \(t\) distribution with 352 degrees of freedom.A standard normal distribution.A \(t\) distribution with 430.231 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0647184414

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 92 observations, they observe:

• \(\overline{X} = 47.15\)
• \(\overline{Y} = 47.05\)
• \(S_X = 1.187\)
• \(S_Y = 0.721\)
• \(S_{XY} = 0.5929\)

Their interest is in whether whether the first device reports higher concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 182 degrees of freedom.A standard normal distribution.A \(t\) distribution with 150.104 degrees of freedom.A \(t\) distribution with 92 degrees of freedom.A \(t\) distribution with 91 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0001715289

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 132 observations, they observe:

• \(\overline{X} = 0.0597\)
• \(\overline{Y} = 0.06\)
• \(S_X = 0.017\)
• \(S_Y = 0.014\)
• \(S_{XY} = 0.0001\)

Their interest is in whether whether the first type of tires exhibit more wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 132 degrees of freedom.A \(t\) distribution with 252.708 degrees of freedom.A \(t\) distribution with 262 degrees of freedom.A standard normal distribution.A \(t\) distribution with 131 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0046449471

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 394 observations, they observe:

• \(\overline{X} = 437.31\)
• \(\overline{Y} = 428.76\)
• \(S_X = 94.11\)
• \(S_Y = 80.3\)
• \(S_{XY} = 216.7682\)

Their interest is in whether whether the stimulant impacts reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 393 degrees of freedom.A \(t\) distribution with 786 degrees of freedom.A \(t\) distribution with 767.004 degrees of freedom.A \(t\) distribution with 394 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0095138679

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 491 observations, they observe:

• \(\overline{X} = 49.96\)
• \(\overline{Y} = 49.94\)
• \(S_X = 1.151\)
• \(S_Y = 1.471\)
• \(S_{XY} = 0.4706\)

Their interest is in whether whether the second device reports higher concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 926.413 degrees of freedom.A standard normal distribution.A \(t\) distribution with 490 degrees of freedom.A \(t\) distribution with 491 degrees of freedom.A \(t\) distribution with 980 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0760162655

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 318 observations, they observe:

• \(\overline{X} = 4.3\)
• \(\overline{Y} = 4.92\)
• \(S_X = 2.81\)
• \(S_Y = 2.65\)
• \(S_{XY} = 0.2361\)

Their interest is in whether whether the individuals in each couple self-report different levels of domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 317 degrees of freedom.A \(t\) distribution with 318 degrees of freedom.A \(t\) distribution with 634 degrees of freedom.A standard normal distribution.A \(t\) distribution with 631.833 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0859992600

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 73 observations, they observe:

• \(\overline{X} = 355.69\)
• \(\overline{Y} = 378.1\)
• \(S_X = 70.34\)
• \(S_Y = 77.33\)
• \(S_{XY} = 2637.74\)

Their interest is in whether whether the stimulant impacts reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 72 degrees of freedom.A \(t\) distribution with 142.727 degrees of freedom.A standard normal distribution.A \(t\) distribution with 73 degrees of freedom.A \(t\) distribution with 144 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0902228372

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 266 observations, they observe:

• \(\overline{X} = 6.62\)
• \(\overline{Y} = 7.18\)
• \(S_X = 3.34\)
• \(S_Y = 6.66\)
• \(S_{XY} = 1.5394\)

Their interest is in whether whether the males self-report doing less domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 265 degrees of freedom.A \(t\) distribution with 266 degrees of freedom.A standard normal distribution.A \(t\) distribution with 530 degrees of freedom.A \(t\) distribution with 390.367 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0446347370

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 357 observations, they observe:

• \(\overline{X} = 111.44\)
• \(\overline{Y} = 112.8\)
• \(S_X = 10.36\)
• \(S_Y = 9.97\)
• \(S_{XY} = 38.8631\)

Their interest is in whether whether the diet increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 356 degrees of freedom.A \(t\) distribution with 357 degrees of freedom.A \(t\) distribution with 712 degrees of freedom.A standard normal distribution.A \(t\) distribution with 710.954 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0754095737

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 148 observations, they observe:

• \(\overline{X} = 53.7\)
• \(\overline{Y} = 54.2\)
• \(S_X = 15.1\)
• \(S_Y = 9.63\)
• \(S_{XY} = 78.5921\)

Their interest is in whether whether the peer tutoring impacts student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 294 degrees of freedom.A \(t\) distribution with 147 degrees of freedom.A standard normal distribution.A \(t\) distribution with 148 degrees of freedom.A \(t\) distribution with 249.604 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0452281831

A farmer hopes to understand the impact of fertilizer application on the productivity of their plots. They consider the application of fertilizer directly to rows of their fields. Within each row, they measure the unfertilized yield (\(X\)) and the fertilized yield (\(Y\)).

In a sample of 45 observations, they observe:

• \(\overline{X} = 80.98\)
• \(\overline{Y} = 78.91\)
• \(S_X = 18.47\)
• \(S_Y = 18.66\)
• \(S_{XY} = 100.7867\)

Their interest is in whether whether the fertilized rows have higher yields.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 44 degrees of freedom.A \(t\) distribution with 87.991 degrees of freedom.A \(t\) distribution with 88 degrees of freedom.A \(t\) distribution with 45 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0034565667

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 342 observations, they observe:

• \(\overline{X} = 103.78\)
• \(\overline{Y} = 101.7\)
• \(S_X = 12.85\)
• \(S_Y = 8.99\)
• \(S_{XY} = 34.6706\)

Their interest is in whether whether the diet changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 682 degrees of freedom.A \(t\) distribution with 342 degrees of freedom.A \(t\) distribution with 341 degrees of freedom.A standard normal distribution.A \(t\) distribution with 610.295 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0232548966

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 312 observations, they observe:

• \(\overline{X} = 10.926\)
• \(\overline{Y} = 10.92\)
• \(S_X = 0.041\)
• \(S_Y = 0.068\)
• \(S_{XY} = 0.0007\)

Their interest is in whether whether calibration changed the diameters of the parts.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 622 degrees of freedom.A \(t\) distribution with 510.725 degrees of freedom.A \(t\) distribution with 312 degrees of freedom.A \(t\) distribution with 311 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.1.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0557924277

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 81 observations, they observe:

• \(\overline{X} = 7.13\)
• \(\overline{Y} = 6.82\)
• \(S_X = 4.27\)
• \(S_Y = 4.26\)
• \(S_{XY} = 7.4558\)

Their interest is in whether whether the males self-report doing more domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 81 degrees of freedom.A \(t\) distribution with 160 degrees of freedom.A standard normal distribution.A \(t\) distribution with 80 degrees of freedom.A \(t\) distribution with 159.999 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0067801833

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 230 observations, they observe:

• \(\overline{X} = 8.55\)
• \(\overline{Y} = 7.91\)
• \(S_X = 2.88\)
• \(S_Y = 6.92\)
• \(S_{XY} = 5.6737\)

Their interest is in whether whether the males self-report doing more domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 458 degrees of freedom.A standard normal distribution.A \(t\) distribution with 230 degrees of freedom.A \(t\) distribution with 306.019 degrees of freedom.A \(t\) distribution with 229 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.2.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0571932293

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 308 observations, they observe:

• \(\overline{X} = 465.31\)
• \(\overline{Y} = 480.13\)
• \(S_X = 83.63\)
• \(S_Y = 97.95\)
• \(S_{XY} = 3874.655\)

Their interest is in whether whether the stimulant increases reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 599.275 degrees of freedom.A standard normal distribution.A \(t\) distribution with 307 degrees of freedom.A \(t\) distribution with 614 degrees of freedom.A \(t\) distribution with 308 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.01.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0965727818

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 483 observations, they observe:

• \(\overline{X} = 468.07\)
• \(\overline{Y} = 466.63\)
• \(S_X = 50.91\)
• \(S_Y = 70.58\)
• \(S_{XY} = 2421.417\)

Their interest is in whether whether the stimulant impacts reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 876.709 degrees of freedom.A \(t\) distribution with 482 degrees of freedom.A \(t\) distribution with 964 degrees of freedom.A \(t\) distribution with 483 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0161977979

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 246 observations, they observe:

• \(\overline{X} = 10.883\)
• \(\overline{Y} = 10.879\)
• \(S_X = 0.074\)
• \(S_Y = 0.023\)
• \(S_{XY} = 0.0003\)

Their interest is in whether whether the parts were larger in diameter before calibration.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 490 degrees of freedom.A \(t\) distribution with 245 degrees of freedom.A \(t\) distribution with 291.898 degrees of freedom.A standard normal distribution.A \(t\) distribution with 246 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0209494900

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 264 observations, they observe:

• \(\overline{X} = 0.0853\)
• \(\overline{Y} = 0.0825\)
• \(S_X = 0.02\)
• \(S_Y = 0.01\)
• \(S_{XY} = 0.0001\)

Their interest is in whether whether the two types of tires exhibit different wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 264 degrees of freedom.A \(t\) distribution with 526 degrees of freedom.A \(t\) distribution with 386.765 degrees of freedom.A \(t\) distribution with 263 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0451472537

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 281 observations, they observe:

• \(\overline{X} = 10.406\)
• \(\overline{Y} = 10.396\)
• \(S_X = 0.03\)
• \(S_Y = 0.078\)
• \(S_{XY} = 0.0005\)

Their interest is in whether whether calibration changed the diameters of the parts.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 361.066 degrees of freedom.A \(t\) distribution with 560 degrees of freedom.A \(t\) distribution with 280 degrees of freedom.A \(t\) distribution with 281 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0185596745

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 237 observations, they observe:

• \(\overline{X} = 0.2604\)
• \(\overline{Y} = 0.26\)
• \(S_X = 0.015\)
• \(S_Y = 0.019\)
• \(S_{XY} = 0.0001\)

Their interest is in whether whether the two types of tires exhibit different wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 236 degrees of freedom.A \(t\) distribution with 472 degrees of freedom.A standard normal distribution.A \(t\) distribution with 237 degrees of freedom.A \(t\) distribution with 447.876 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0606475910

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 410 observations, they observe:

• \(\overline{X} = 43.2\)
• \(\overline{Y} = 43\)
• \(S_X = 17.02\)
• \(S_Y = 8.08\)
• \(S_{XY} = 83.8985\)

Their interest is in whether whether the peer tutoring impacts student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 409 degrees of freedom.A \(t\) distribution with 818 degrees of freedom.A \(t\) distribution with 410 degrees of freedom.A \(t\) distribution with 584.444 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0424520742

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 349 observations, they observe:

• \(\overline{X} = 294.54\)
• \(\overline{Y} = 303.61\)
• \(S_X = 72.09\)
• \(S_Y = 58.79\)
• \(S_{XY} = 548.0599\)

Their interest is in whether whether the stimulant increases reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 348 degrees of freedom.A standard normal distribution.A \(t\) distribution with 668.931 degrees of freedom.A \(t\) distribution with 349 degrees of freedom.A \(t\) distribution with 696 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0784542003

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 277 observations, they observe:

• \(\overline{X} = 11.522\)
• \(\overline{Y} = 11.52\)
• \(S_X = 0.061\)
• \(S_Y = 0.032\)
• \(S_{XY} = 0.0007\)

Their interest is in whether whether the parts were larger in diameter before calibration.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 552 degrees of freedom.A \(t\) distribution with 277 degrees of freedom.A \(t\) distribution with 417.213 degrees of freedom.A \(t\) distribution with 276 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0353292719

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 237 observations, they observe:

• \(\overline{X} = 46.56\)
• \(\overline{Y} = 46.48\)
• \(S_X = 0.24\)
• \(S_Y = 1.453\)
• \(S_{XY} = 0.243\)

Their interest is in whether whether the two devices report different concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 237 degrees of freedom.A \(t\) distribution with 248.868 degrees of freedom.A standard normal distribution.A \(t\) distribution with 236 degrees of freedom.A \(t\) distribution with 472 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0134706282

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 84 observations, they observe:

• \(\overline{X} = 8.76\)
• \(\overline{Y} = 6.57\)
• \(S_X = 4.58\)
• \(S_Y = 8.05\)
• \(S_{XY} = 1.7601\)

Their interest is in whether whether the males self-report doing more domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 84 degrees of freedom.A standard normal distribution.A \(t\) distribution with 83 degrees of freedom.A \(t\) distribution with 131.638 degrees of freedom.A \(t\) distribution with 166 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0127028448

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 210 observations, they observe:

• \(\overline{X} = 5.76\)
• \(\overline{Y} = 6\)
• \(S_X = 1.3\)
• \(S_Y = 9\)
• \(S_{XY} = 5.7749\)

Their interest is in whether whether the males self-report doing more domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 217.717 degrees of freedom.A standard normal distribution.A \(t\) distribution with 210 degrees of freedom.A \(t\) distribution with 418 degrees of freedom.A \(t\) distribution with 209 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.11.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0177451408

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 480 observations, they observe:

• \(\overline{X} = 0.2977\)
• \(\overline{Y} = 0.2981\)
• \(S_X = 0.003\)
• \(S_Y = 0.003\)
• \(S_{XY} = 0\)

Their interest is in whether whether the first type of tires exhibit less wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 479 degrees of freedom.A \(t\) distribution with 958 degrees of freedom.A \(t\) distribution with 480 degrees of freedom.A \(t\) distribution with 958 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0427670869

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 259 observations, they observe:

• \(\overline{X} = 105.33\)
• \(\overline{Y} = 104.84\)
• \(S_X = 7.75\)
• \(S_Y = 7.82\)
• \(S_{XY} = 15.3778\)

Their interest is in whether whether the medication increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 515.958 degrees of freedom.A standard normal distribution.A \(t\) distribution with 258 degrees of freedom.A \(t\) distribution with 516 degrees of freedom.A \(t\) distribution with 259 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0587131035

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 228 observations, they observe:

• \(\overline{X} = 11.039\)
• \(\overline{Y} = 11.029\)
• \(S_X = 0.036\)
• \(S_Y = 0.049\)
• \(S_{XY} = 0.0004\)

Their interest is in whether whether the parts were larger in diameter before calibration.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 228 degrees of freedom.A \(t\) distribution with 454 degrees of freedom.A \(t\) distribution with 416.768 degrees of freedom.A \(t\) distribution with 227 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0518975205

A farmer hopes to understand the impact of fertilizer application on the productivity of their plots. They consider the application of fertilizer directly to rows of their fields. Within each row, they measure the unfertilized yield (\(X\)) and the fertilized yield (\(Y\)).

In a sample of 66 observations, they observe:

• \(\overline{X} = 104.14\)
• \(\overline{Y} = 99.39\)
• \(S_X = 14.37\)
• \(S_Y = 15.7\)
• \(S_{XY} = 36.8332\)

Their interest is in whether whether the fertilizer impacts the yields of the rows.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 65 degrees of freedom.A \(t\) distribution with 130 degrees of freedom.A standard normal distribution.A \(t\) distribution with 66 degrees of freedom.A \(t\) distribution with 128.995 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.15.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0467495794

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 494 observations, they observe:

• \(\overline{X} = 30.46\)
• \(\overline{Y} = 30.45\)
• \(S_X = 0.868\)
• \(S_Y = 0.517\)
• \(S_{XY} = 0.0921\)

Their interest is in whether whether the first device reports higher concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 986 degrees of freedom.A \(t\) distribution with 803.695 degrees of freedom.A \(t\) distribution with 493 degrees of freedom.A \(t\) distribution with 494 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0626628390

A manufacturing company decides to recalibrate settings for one type of their machines. They want to determine how this calibration has impacted the dimensions of a particular component being manufactured. They take diameter measurements produced by each of these machines both before (\(X\)) and after (\(Y\)) calibration.

In a sample of 203 observations, they observe:

• \(\overline{X} = 11.6\)
• \(\overline{Y} = 11.593\)
• \(S_X = 0.058\)
• \(S_Y = 0.067\)
• \(S_{XY} = 0.0009\)

Their interest is in whether whether the parts were larger in diameter before calibration.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 202 degrees of freedom.A \(t\) distribution with 395.876 degrees of freedom.A \(t\) distribution with 203 degrees of freedom.A standard normal distribution.A \(t\) distribution with 404 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0794298265

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 339 observations, they observe:

• \(\overline{X} = 116.03\)
• \(\overline{Y} = 117.65\)
• \(S_X = 12.52\)
• \(S_Y = 9.37\)
• \(S_{XY} = 52.2836\)

Their interest is in whether whether the medication increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 626.214 degrees of freedom.A \(t\) distribution with 676 degrees of freedom.A \(t\) distribution with 338 degrees of freedom.A \(t\) distribution with 339 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0942465650

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 279 observations, they observe:

• \(\overline{X} = 0.0619\)
• \(\overline{Y} = 0.0636\)
• \(S_X = 0.005\)
• \(S_Y = 0.011\)
• \(S_{XY} = 0\)

Their interest is in whether whether the two types of tires exhibit different wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 388.173 degrees of freedom.A \(t\) distribution with 278 degrees of freedom.A \(t\) distribution with 279 degrees of freedom.A \(t\) distribution with 556 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0715732769

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 428 observations, they observe:

• \(\overline{X} = 49.6\)
• \(\overline{Y} = 50.2\)
• \(S_X = 13.18\)
• \(S_Y = 9.8\)
• \(S_{XY} = 70.1448\)

Their interest is in whether whether the peer tutoring impacts student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 428 degrees of freedom.A \(t\) distribution with 788.616 degrees of freedom.A \(t\) distribution with 427 degrees of freedom.A \(t\) distribution with 854 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0560424108

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 206 observations, they observe:

• \(\overline{X} = 19.3\)
• \(\overline{Y} = 19.35\)
• \(S_X = 1.053\)
• \(S_Y = 1.987\)
• \(S_{XY} = 0.5967\)

Their interest is in whether whether the two devices report different concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 311.727 degrees of freedom.A \(t\) distribution with 410 degrees of freedom.A standard normal distribution.A \(t\) distribution with 206 degrees of freedom.A \(t\) distribution with 205 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0086986199

A farmer hopes to understand the impact of fertilizer application on the productivity of their plots. They consider the application of fertilizer directly to rows of their fields. Within each row, they measure the unfertilized yield (\(X\)) and the fertilized yield (\(Y\)).

In a sample of 265 observations, they observe:

• \(\overline{X} = 100.19\)
• \(\overline{Y} = 98.72\)
• \(S_X = 11.14\)
• \(S_Y = 17.81\)
• \(S_{XY} = 12.1476\)

Their interest is in whether whether the unfertilized rows have higher yields.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 528 degrees of freedom.A \(t\) distribution with 264 degrees of freedom.A \(t\) distribution with 265 degrees of freedom.A \(t\) distribution with 443.152 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0355266295

A laboratory wants to compare two different devices for measuring the concentrations of chemical solutions. They prepare multiple samples, measuring each individual sample with each device. They report the measured concentrations of the first device as \(X\) and the measured concentrations of the second device as \(Y\).

In a sample of 380 observations, they observe:

• \(\overline{X} = 14.21\)
• \(\overline{Y} = 14.38\)
• \(S_X = 1.907\)
• \(S_Y = 0.292\)
• \(S_{XY} = 0.2878\)

Their interest is in whether whether the second device reports higher concentrations, on average.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 758 degrees of freedom.A \(t\) distribution with 380 degrees of freedom.A \(t\) distribution with 396.762 degrees of freedom.A \(t\) distribution with 379 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0631583599

A farmer hopes to understand the impact of fertilizer application on the productivity of their plots. They consider the application of fertilizer directly to rows of their fields. Within each row, they measure the unfertilized yield (\(X\)) and the fertilized yield (\(Y\)).

In a sample of 124 observations, they observe:

• \(\overline{X} = 103.55\)
• \(\overline{Y} = 106.29\)
• \(S_X = 17.79\)
• \(S_Y = 10.23\)
• \(S_{XY} = 116.5187\)

Their interest is in whether whether the fertilized rows have higher yields.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 124 degrees of freedom.A \(t\) distribution with 246 degrees of freedom.A standard normal distribution.A \(t\) distribution with 196.328 degrees of freedom.A \(t\) distribution with 123 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.02.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0922866985

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 334 observations, they observe:

• \(\overline{X} = 115.6\)
• \(\overline{Y} = 116.59\)
• \(S_X = 8.68\)
• \(S_Y = 11.78\)
• \(S_{XY} = 60.3665\)

Their interest is in whether whether the diet increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 612.272 degrees of freedom.A \(t\) distribution with 334 degrees of freedom.A standard normal distribution.A \(t\) distribution with 333 degrees of freedom.A \(t\) distribution with 666 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0907939425

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 432 observations, they observe:

• \(\overline{X} = 0.0933\)
• \(\overline{Y} = 0.0935\)
• \(S_X = 0.009\)
• \(S_Y = 0.007\)
• \(S_{XY} = 0\)

Their interest is in whether whether the first type of tires exhibit more wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 432 degrees of freedom.A \(t\) distribution with 862 degrees of freedom.A \(t\) distribution with 431 degrees of freedom.A \(t\) distribution with 812.754 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0995157391

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 387 observations, they observe:

• \(\overline{X} = 101.58\)
• \(\overline{Y} = 100.79\)
• \(S_X = 7.72\)
• \(S_Y = 8.06\)
• \(S_{XY} = 20.0012\)

Their interest is in whether whether the diet lowers patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 772 degrees of freedom.A \(t\) distribution with 770.57 degrees of freedom.A \(t\) distribution with 387 degrees of freedom.A \(t\) distribution with 386 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0771291801

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 416 observations, they observe:

• \(\overline{X} = 102.65\)
• \(\overline{Y} = 102.06\)
• \(S_X = 8.28\)
• \(S_Y = 10.25\)
• \(S_{XY} = 1.3323\)

Their interest is in whether whether the medication changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 416 degrees of freedom.A \(t\) distribution with 794.862 degrees of freedom.A \(t\) distribution with 415 degrees of freedom.A \(t\) distribution with 830 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0592940943

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 96 observations, they observe:

• \(\overline{X} = 122.95\)
• \(\overline{Y} = 122.15\)
• \(S_X = 12.33\)
• \(S_Y = 7.21\)
• \(S_{XY} = 23.3929\)

Their interest is in whether whether the diet changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 190 degrees of freedom.A standard normal distribution.A \(t\) distribution with 153.167 degrees of freedom.A \(t\) distribution with 96 degrees of freedom.A \(t\) distribution with 95 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.14.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0855656289

A group of researchers are studying the impact of a newly designed medication on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(Y\)) taking the medication.

In a sample of 283 observations, they observe:

• \(\overline{X} = 101.54\)
• \(\overline{Y} = 100.12\)
• \(S_X = 9.93\)
• \(S_Y = 11.47\)
• \(S_{XY} = 18.3017\)

Their interest is in whether whether the medication lowers patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 283 degrees of freedom.A standard normal distribution.A \(t\) distribution with 282 degrees of freedom.A \(t\) distribution with 564 degrees of freedom.A \(t\) distribution with 552.669 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0642013873

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 401 observations, they observe:

• \(\overline{X} = 7.54\)
• \(\overline{Y} = 6.27\)
• \(S_X = 6.47\)
• \(S_Y = 8.77\)
• \(S_{XY} = 0.9165\)

Their interest is in whether whether the individuals in each couple self-report different levels of domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 401 degrees of freedom.A \(t\) distribution with 800 degrees of freedom.A standard normal distribution.A \(t\) distribution with 735.907 degrees of freedom.A \(t\) distribution with 400 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.17.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0912263102

A farmer hopes to understand the impact of fertilizer application on the productivity of their plots. They consider the application of fertilizer directly to rows of their fields. Within each row, they measure the unfertilized yield (\(X\)) and the fertilized yield (\(Y\)).

In a sample of 431 observations, they observe:

• \(\overline{X} = 83.27\)
• \(\overline{Y} = 81.85\)
• \(S_X = 11.37\)
• \(S_Y = 13.6\)
• \(S_{XY} = 57.0751\)

Their interest is in whether whether the fertilizer impacts the yields of the rows.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 833.818 degrees of freedom.A \(t\) distribution with 860 degrees of freedom.A \(t\) distribution with 431 degrees of freedom.A standard normal distribution.A \(t\) distribution with 430 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.08.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0122290356

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 116 observations, they observe:

• \(\overline{X} = 67.1\)
• \(\overline{Y} = 64.8\)
• \(S_X = 9.11\)
• \(S_Y = 15.96\)
• \(S_{XY} = 80.7139\)

Their interest is in whether whether the peer tutoring impacts student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 230 degrees of freedom.A \(t\) distribution with 182.746 degrees of freedom.A \(t\) distribution with 116 degrees of freedom.A standard normal distribution.A \(t\) distribution with 115 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.09.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.

Question ID: 0641603191

A manufacturer of tires is interested in determining the quality difference in two different makes of their tires. They decide to take pairs of the tires, placing 2 of each type on the same set of vehicles, driving and measuring the wear. They record the wear of the first type as \(X\) and of the second type as \(Y\).

In a sample of 437 observations, they observe:

• \(\overline{X} = 0.084\)
• \(\overline{Y} = 0.0838\)
• \(S_X = 0.014\)
• \(S_Y = 0.004\)
• \(S_{XY} = 0\)

Their interest is in whether whether the first type of tires exhibit more wear.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 436 degrees of freedom.A \(t\) distribution with 437 degrees of freedom.A \(t\) distribution with 506.712 degrees of freedom.A \(t\) distribution with 872 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.04.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0048432780

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 227 observations, they observe:

• \(\overline{X} = 122.5\)
• \(\overline{Y} = 122.76\)
• \(S_X = 8.44\)
• \(S_Y = 9.07\)
• \(S_{XY} = 29.6227\)

Their interest is in whether whether the diet increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 449.678 degrees of freedom.A \(t\) distribution with 227 degrees of freedom.A \(t\) distribution with 452 degrees of freedom.A \(t\) distribution with 226 degrees of freedom.A standard normal distribution.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.05.

Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0855733926

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 187 observations, they observe:

• \(\overline{X} = 129.36\)
• \(\overline{Y} = 128.61\)
• \(S_X = 7.43\)
• \(S_Y = 10.05\)
• \(S_{XY} = 39.3795\)

Their interest is in whether whether the diet changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 186 degrees of freedom.A standard normal distribution.A \(t\) distribution with 187 degrees of freedom.A \(t\) distribution with 342.555 degrees of freedom.A \(t\) distribution with 372 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.13.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0040116600

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 252 observations, they observe:

• \(\overline{X} = 109.5\)
• \(\overline{Y} = 108.86\)
• \(S_X = 9.47\)
• \(S_Y = 12.84\)
• \(S_{XY} = 69.618\)

Their interest is in whether whether the diet changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 502 degrees of freedom.A \(t\) distribution with 251 degrees of freedom.A \(t\) distribution with 252 degrees of freedom.A \(t\) distribution with 461.719 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.19.

Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0541937648

A psychologist is interested in how a particular stimulant impacts individual reaction times. The psychologist administer a test to individuals, and records their reaction times, both before (\(X\)) and after (\(Y\)) receiving the stimulant.

In a sample of 406 observations, they observe:

• \(\overline{X} = 431.01\)
• \(\overline{Y} = 426.72\)
• \(S_X = 82.08\)
• \(S_Y = 80.29\)
• \(S_{XY} = 3428.851\)

Their interest is in whether whether the stimulant increases reaction times.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 810 degrees of freedom.A standard normal distribution.A \(t\) distribution with 809.607 degrees of freedom.A \(t\) distribution with 406 degrees of freedom.A \(t\) distribution with 405 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.03.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0002762068

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 389 observations, they observe:

• \(\overline{X} = 129.59\)
• \(\overline{Y} = 129.41\)
• \(S_X = 8.01\)
• \(S_Y = 8.38\)
• \(S_{XY} = 29.466\)

Their interest is in whether whether the diet changes patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 389 degrees of freedom.A \(t\) distribution with 776 degrees of freedom.A \(t\) distribution with 388 degrees of freedom.A standard normal distribution.A \(t\) distribution with 774.423 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.

Question ID: 0979913268

A team of researchers is interested in the perceived breakdown of domestic labour within heterosexual couples. The researchers recruit a range of couples, asking them to self-report their perceived quantity of weekly household labour. The researchers record the male-reported values as \(X\), and the female reported values as \(Y\).

In a sample of 85 observations, they observe:

• \(\overline{X} = 7.4\)
• \(\overline{Y} = 7.94\)
• \(S_X = 8.69\)
• \(S_Y = 9.22\)
• \(S_{XY} = 39.4843\)

Their interest is in whether whether the males self-report doing more domestic labour.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A \(t\) distribution with 168 degrees of freedom.A standard normal distribution.A \(t\) distribution with 167.415 degrees of freedom.A \(t\) distribution with 85 degrees of freedom.A \(t\) distribution with 84 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.12.

Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.

Question ID: 0788645628

A school is implementing a peer tutoring service to see if it has an impact on student test scores on a standardized test. For the students in the peer tutoring service, the school records the test scores before (\(X\)) and after (\(Y\)) the tutoring takes place.

In a sample of 203 observations, they observe:

• \(\overline{X} = 63.7\)
• \(\overline{Y} = 63.3\)
• \(S_X = 11.54\)
• \(S_Y = 8.26\)
• \(S_{XY} = 64.4125\)

Their interest is in whether whether the peer tutoring improves student test scores.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X > \mu_Y\) vs. \(H_A: \mu_X \leq \mu_Y\)\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 203 degrees of freedom.A \(t\) distribution with 365.948 degrees of freedom.A \(t\) distribution with 202 degrees of freedom.A \(t\) distribution with 404 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.07.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.

Question ID: 0079136553

A group of researchers are studying the impact of a particular diet on blood pressure. They measure individuals’ systolic blood pressure before (\(X\)) and after (\(X\)) starting the diet.

In a sample of 205 observations, they observe:

• \(\overline{X} = 123.26\)
• \(\overline{Y} = 125.07\)
• \(S_X = 11\)
• \(S_Y = 8.87\)
• \(S_{XY} = 19.6436\)

Their interest is in whether whether the diet increases patients’ average systolic blood pressure.

1. What set of hypotheses should be tested in this setting?

\(H_0: \mu_X \geq \mu_Y\) vs. \(H_A: \mu_X < \mu_Y\)\(H_0: \mu_X < \mu_Y\) vs. \(H_A: \mu_X \geq \mu_Y\)\(H_0: \mu_X \leq \mu_Y\) vs. \(H_A: \mu_X > \mu_Y\)\(H_0: \mu_X \neq \mu_Y\) vs. \(H_A: \mu_X = \mu_Y\)\(H_0: \mu_X = \mu_Y\) vs. \(H_A: \mu_X \neq \mu_Y\)

2. What is the value of the test statistic used to test the hypothesis identified in (a)?
3. What is the relevant sampling distribution for this hypothesis test?

A standard normal distribution.A \(t\) distribution with 408 degrees of freedom.A \(t\) distribution with 205 degrees of freedom.A \(t\) distribution with 390.458 degrees of freedom.A \(t\) distribution with 204 degrees of freedom.

3. What is the \(p\)-value computed for the hypothesis test?
4. What is the conclusion from the hypothesis test, at a significance level of 0.06.

Because the \(p\)-value is greater than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we accept the null hypothesis.Because the \(p\)-value is smaller than \(\alpha\), we reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we fail to reject the null hypothesis.Because the \(p\)-value is greater than \(\alpha\), we reject the null hypothesis.

Question ID: 0170479136

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1. For instance, we may wish to compare two different treatments or two different interventions; we may wish to consider whether one group is different from another, or whether one process performs the same as another; etc.

2. Such as \(\mu\) or \(\sigma^2\).

3. Note, \(\Delta = E[X] - E[Y]\) is a population parameter, one that depends on the joint distribution of \(X\) and \(Y\).

4. It will be unbiased for the same reasons that \(\widehat{\Delta}\) was.

5. Or any of the other variations on this test.

6. This can happen, for instance, when you are measuring the same trait in two different populations, but where the variability of the trait is quite well understood.

7. As a reminder, the covariance between two random variables is a measure of their relationship. A positive covariance means that there is a positive relationship between the quantities, where \(Y\) increases as \(X\) increases. A negative has the opposite effect. If two random variables are independent, then they have covariance \(0\).