use the Kruskal - Wallis test?. Triathlon Times? Jeff Parent is a statistics instructor who participates in triathlons. Listed below are times (in minutes and seconds) he recorded while riding a bicycle for five laps through each mile of a 3-mile loop. Use a 0.05 significance level to test the claim that the samples are from populations with the same median. What do the data suggest? Mile 1 3:15 3:24 3:23 3:22 3:21 Mile 2 3:19 3:22 3:21 3:17 3:19 Mile 3 3:34 3:31 3:29 3:31 3:29

Solution 5BSC Step 1 Kruskal-Wallis test satisfies the following two requirements. 1. Sample data must be independent and drawn according to simple random sampling. 2. Each sample must contain minimum of five entries. By using the data from exercise, we see that the samples are drawn at random, where the three Mile loop are independent to each other. Hence the first requirement is satisfied. Now, we see that the sample size of Mile 1 is 5, sample size of Mile 2 is 5 and sample size of Mile 3 is 5. Hence the second requirement is satisfied. Therefore, the two requirements of Kruskal-Wallis test are satisfied. Step 2 By using = 0.05 level of significance we need t o test the claim that the samples are from populations with the same median. The Hypotheses can be expressed as H0 The samples are from population with the same median. H1 The samples are from population with the different median. All these three mile with Mile 1, Mile 2, Mile 3 samples are combined together to get a big sample. We first order the absolute values of the difference scores and assign rank from 1 through ‘n’ to the smallest through largest absolute values of the difference scores, and assign the mean rank when there are ties in the absolute values of the difference scores. Mile 1 Mile 2 Mile 3 3:15(1) 3:19(3.5) 3:34(15) 3:24(10) 3:22(7.5) 3:31(13.5) 3:23(7.5) 3:21(5.5) 3:29(11.5) 3:22(7.5) 3:17(2) 3:31(13.5) 3:21(5.5) 3:19(3.5) 3:29(11.5) The smallest value is assigned as the rank 1, here 3:15 is the smallest value and so on up to the largest value 3:34 is assigned as rank 15.