Question 1: Suppose that 11 individuals take the GMAT (Graduate Management Admission Test), then take a GMAT preparation course, and then take the GMAT again. Of the 11 individuals in the sample, 9improved their score, 1 individual scored lower, and 1 individual's score was unchanged. Using a significance level of 0.05, can we conclude from this information that the preparation course is successful in improving individuals' performance on the GMAT?
Question 2: The following eight observations were randomly selected from two populations that were not necessarily normally distributed.
Population 1: 38, 45, 56, 57, 61, 69, 70, 79
Population 2: 26, 31, 35, 42, 51, 52, 57, 62
Using a significance level of 0.1, carry out a two-tailed Wilcoxon rank-sum test to determine whether there is a difference between the two populations.