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Suppose you want to use the Wilcoxon rank sum test to detect a shift in distribution 1 to the right of distribution 2 based on samples of size \(n_{1}=6\) and \(n_{2}=8\) a. Should you use \(T_{1}\) or \(T_{1}^{*}\) as the test statistic? b. What is the rejection region for the test if \(\alpha=.05 ?\) c. What is the rejection region for the test if \(\alpha=.01 ?\)

A paired-difference experiment was conducted to compare two populations. The data are shown in the table. Use a sign test to determine whether the population distributions are different. a. State the null and alternative hypotheses for the test. b. Determine an appropriate rejection region with \(\alpha \approx .01\) c. Calculate the observed value of the test statistic. d. Do the data present sufficient evidence to indicate that populations 1 and 2 are different?

Eight people were asked to perform a simple puzzle-assembly task under normal conditions and under stressful conditions. During the stressful time, a mild shock was delivered to subjects 3 minutes after the start of the experiment and every 30 seconds thereafter until the task was completed. Blood pressure readings were taken under both conditions. The data in the table are the highest readings during the experiment. Do the data present sufficient evidence to indicate higher blood pressure readings under stressful conditions? Analyze the data using the Wilcoxon signed-rank test for a paired experiment.