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 five 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 Coatings II III IV 39.12 62.48 43.20 64.39 41.56 59.50 45.37 50.16 Times 45.03 60.22 45.03 56.39 42.33 56.13 39.19 61.20 43.28 55.34 46.48 55.45 a. Using R, produce a high-quality graph to compare the shoe tread coatings. Interpret the results from the graph. b. Test whether the shoe tread coatings affect the runners' times. What significance level can you use to perform this test? c. Test for the significance of the contrast that the average of twice the first coating with the second and third coatings equals four-thirds of the fourth coating. Use a 1% significance level and include all your steps (e.g., hypothesis statements, test statistics, etc.). Hint: In R, using pf(q, df1, df2, lower. tail=FALSE) where q is your test statistic provides the p-value for an F-test