2 (14 pts) Suppose we have data on vitamin E intake (IU/day) (from both diet and vitamin E supplements) at baseline in four treatment groups in a clinical trial of nutritional supplements. It is important to establish that the vitamin E intakes of the four treatment groups are comparable at baseline. The data (baseline vitamin E intake) for the first 10 participants in each group are given below. A29 Subject Group 1 Group 2 Group 3 Group 4 15.92 5.22 8.24 3.29 16.31 17.27 3.67 6.19 16.24 7.95 15.21 109.17 4.02 8.25 5.82 6.12 18.33 5.60 14.12 159.90 16.27 5.29 6.00 5.38 55.99 10.64 7.17 OOOOO 4.42 12.20 3.33 Part a We wish to assess whether there are significant overall group differences in vitamin E intake. Why might a nonparametric analysis of these data be useful? Please make a compelling argument (possibly including a graph to support your argument). Part b Use the Kruskal-Wallis test to assess whether there are significant overall group differences in vitamin E intake. Report a p-value correct to 4 decimal places and an appropriate conclusion in the context of the problem. Part c To compare the ith and jth treatment groups under the Kruskal-Wallis test, use the following procedure (called the Dunn procedure): Step 1: Compute z - R, N(N +1). (+ -) Step 2: For a two-sided test with significance level a, p-value = 2.P(Z >21) where 2 N(0,1). If you found significant results in Part b, then use the Dunn procedure to identify which specific groups are significantly different. List out all pairs of groups that are significantly different from each other in terms of vitamin E measurements