study to decide whether support groups improve (2) A researcher conducts a academic performance for at-risk high school students. Ten such students are ran- domly selected to take part in the support group for a semester, while the other 10 at-risk students serve as a control group. At the end of the semester, the improve- ment in GPA versus the previous semester is recorded for each student. Support Group: 0.5, 0.8, 0.7, 0.7, -0.1, 0.2, 0.4, 0.4, 0.5, 0.4 Control Group: -0.3, 0.0, -0.1, 0.2, -0.1, -0.2, -0.2, 0.0, -0.1, 0.1 (a) At the 5% level, test whether there is evidence of a difference in variance between the two groups. Assume normality for this test.You may use R for to conduct the test, but you need to write your hypotheses, the test statistic, the p-value, and the decision/conclusion in the context of the problem (b) At the 10% level, test whether there is evidence that the true mean GPA increase is higher for the students who were in the support group. Use the results of part a) to inform your decision of whether to pool (or not). You may use R for to conduct the test, but you need to write your hypotheses, the test statistic, the p-value, and the decision/conclusion in the context of the problem (c) At the 10% level, groups. You may use R for to conduct the test, but you need to write your hypotheses, the test statistic, the p-value, and the decision/conclusion in the context of the problem.Comment on how this test differs from the test in part b) use the Wilcoxon-Mann-Whitney test to compare the two End