use the Kruskal - Wallis test?. Highway Fuel Consumption? Listed below are highway fuel consumption amounts (mi/gal) for cars categorized by the sizes of small, midsize, and large (from Data Set 14 in Appendix B). Using a 0.05 significance level, test the claim that the three size categories have the same median highway fuel consumption. Does the size of a car appear to affect highway fuel consumption? Small??28?26?23?24?26?24?25 Midsize?28?31?26?30?28?29?31 Large??34?36?28?40?33?35?26

Solution 8BSC 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 samples are independent to each other. Hence the first requirement is satisfied. Now, we see that the sample size of Small is 7, sample size of Midsize is 7 and sample size of Large is 7. 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 different size categories have the same median chest deceleration in the standard crash test The Hypotheses can be expressed as H : the three size categories have the same median highway fuel consumption 0 H1 the three size categories have the different median highway fuel consumption Small28262324262425 Midsize28312630282931 Large34362840333526 Midsiz Small Rank Rank Large Rank e 28 10.5 28 10.5 34 18 26 6.5 31 15.5 36 20 23 1 26 6.5 28 10.5 24 2.5 30 14 40 21 26 6.5 28 10.5 33 17 24 2.5 29 13 35 19 25 4 31 15.5 26 6.5 All these three 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 ānā 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. The smallest value is assigned as the rank 1, here 23 is the smallest value and so on up to the largest value 40 is assigned as rank 21.