6) Nike, Inc. is developing a new running shoe for the 400m dash. Twenty of those running shoes were randomly divided into four groups of ve shoes. The running shoe treads in each group were coated with one of four types of coating (labelled I, II, III, IV). The 400m dash times (in seconds) for one runner wearing each shoe was the outcome variable in the experiment. The data are given in the table below. Shoe Tread Coatins --I--IE- 39.12 62.48 43.20 41.56 59.50 45.37 50.16 Times 56.39 42.33 56.13 39.19 61.20 43.28 55.34 46.43 55.45 a. Using R, produce a high-quality graph to compare the shoe tread coatings. InteIpret the results from the graph. b. Test whether the shoe tread coatings affect the runners' times. What signicance level can you use to perform this test? 0. Test for the signicance of the contrast that the average of twice the rst coating with the second and third coatings equals four-thirds of the fourth coating. Use a 1% signicance level and include all your steps (e.g., hypothesis statements, test statistics, etc.). Hint: In R, using p'F(q, dFl, df2 , 1ower . ta'i1:FALSE) where q is your test statistic provides the p-value for an F-test