Exam 10: Inferences for Two Population Means

Students take a math test before and after tutoring. The data for a random sample of students is given below. Before 54 72 63 82 51 80 63 36 44 After 68 70 67 78 55 83 63 52 40 Suppose that you want to use these data to perform a hypothesis test to determine whether the mean score before the tutoring is lower than the mean score after the tutoring. Conduct preliminary graphical data analyses to decide whether it is reasonable to apply the paired t-test and whether it is reasonable to apply the paired Wilcoxon signed-rank test or whether neither test is reasonable. If both tests are reasonable,which test would be preferable? Explain your thinking.

Suppose that you want to perform a hypothesis test to compare the means of two populations using a paired sample. Preliminary data analyses of the sample of paired differences suggest that the distribution of the paired-difference variable is skewed to the right . The sample of 20 paired differences contains an outlier. If it is not legitimate to remove the outlier, is it reasonable to use a paired t-test? Is it reasonable to use a paired Wilcoxon signed-rank test? Explain your thinking

Use the Mann-Whitney Table to find the critical values. For a left-tailed or two-tailed test, you will also need the relation $M _ { 1 - A } = n _ { 1 } \left( n _ { 1 } + n _ { 2 } + 1 \right) - M _ { A }$ . - $\mathrm { n } _ { 1 } = 8 , \mathrm { n } _ { 2 } = 5$ , significance level $= 0.01$ , right-tailed test