Explanation Given info: The data shows several veterinarians in each state and their salaries. Calculation: State the null and alternative hypothesis. Null hypothesis: H 0 : The distribution of veterinarians’ salaries is the same in all the three states. Alternative hypothesis: H 1 : The distribution of the veterinarians’ salaries in at least one state is different from the others. Critical value: d .f = k − 1 = 3 − 1 = 2 From the table, “critical values for Kruskal-Wallis Test” with α = 0.05 and d .f . = 2 ; the critical value is χ 0 2 = 5.991 . Thus, the rejection region is χ 2 > 5.991 . Condition: If H is in the rejection, then reject H 0 . Otherwise, fail to reject H 0 . Test statistic: The sample size for sample 1 is 10. The sample size for sample 2 is 9. The sample size for sample 3 is 9 The table shows the combined data in ascending order and its rank. Ordered data Sample Rank 57.6 3 1 63.3 1 2 74.8 1 3 80.4 2 4 83.4 3 5 84.7 2 6 85.3 1 7 89.6 1 8 91.0 1 9 95.0 2 10 97.9 1 11 101.1 1 12 105.3 2 13 106.7 2 14 111.3 3 15 113.2 3 16 116.6 2 17 118.7 1 18 121.6 2 19 126.8 3 20 131.0 3 21 135.9 2 22 143.3 2 23 146.1 3 24 147.7 1 25 149.9 1 26 154.0 3 27 160.2 3 28 For three or more independent samples, the test statistic for the Kruskal-Wallis test is H = 12 N ( N + 1 ) ( R 1 2 n 1 + R 2 2 n 2 + R 3 2 n 3 + ... + R k 2 n k ) − 3 ( N + 1 ) Where k is the number of samples, n i is the size of the i t h sample, N is the sum of the sample sizes, and R i is the sum of the ranks of the i t h sample

Elementary Statistics 7th.ed. Instructor's Review Copy

7th Edition

ISBN: 9780134683584

Author: Larson

Publisher: PEARSON

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Chapter 11.3, Problem 1TY

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To test: The claim that the distribution of the veterinarians’ salaries in at least one state is different from the others.

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Chapter 11.2, Problem 7CS

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Elementary Statistics 7th.ed. Instructor's Review Copy

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To test: The claim that the distribution of the veterinarians’ salaries in at least one state is different from the others.

Solution Summary: The author states that there is not enough evidence to conclude that the distribution of veterinarians' salaries in the three states are different.

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To test: The claim that the distribution of the veterinarians’ salaries in at least one state is different from the others.

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Chapter 11 Solutions