Explanation The test hypothesis is given as follows: Null hypothesis: H 0 : There is no difference in the mobility in the four industries. Alternative hypothesis: H 1 : There is a difference in the mobility in the four industries. Here, the test statistic H follows the chi-square distribution with k − 1 degrees of freedom, where k is the number of populations and H is the test statistic. In order to formulate the decision rule, the chi-square is used. In this context, the number of populations is 4. Degrees of freedom for populations: k − 1 = 4 − 1 = 3 From Appendix B, Table B.7 Critical Values of Chi-Square: Procedure: 1. In the table, first locate the 3 in the first z column. 2. Locate the value of 0.05 in the second row. 3. Locate the value; the intersection of the row and column values gives the critical value. The critical value for 3 df for 0.05 significance level is 7.815. Decision rule: If H > 7.815 , reject the null hypothesis. Otherwise fail to reject the null hypothesis. In this context, the test statistic for Kruskal–Wallis test is denoted as H . Test statistic, H : H = 12 n ( n + 1 ) [ ( ∑ R 1 ) 2 n 1 + ( ∑ R 2 ) 2 n 2 + ... + ( ∑ R k ) 2 n k ] − 3 ( n + 1 ) . Here, k is the number of populations, R 1 , R 2 , ... R k is ranks of samples 1, 2,… k . n 1 , n 2 , ... n k is sizes of samples 1, 2,… k . n is the combined number of observations for all samples. In this context, it is necessary to rank all the observations. The following table represents the ranks of all the samples: Chemical Rank 1 Retail Rank 2 Internet Rank 3 Aerospace Rank 4 4 2 3 1 62 18 30 11 17 6.5 12 4 40 15 38 13 8 3 40 15 81 20 46 17 20 9 17 6.5 96 21 40 15 16 5 31 12 76 19 21 10 19 8 Here, the sum of Rank 1 is given below: ∑ R 1 = 2 + 6

Statistical Techniques in Business and Economics

16th Edition

ISBN: 9780077639723

Author: Lind

Publisher: Mcgraw-Hill Course Content Delivery

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Chapter 16, Problem 37CE

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Chapter 16, Problem 36CE

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Statistical Techniques in Business and Economics

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State whether there is a difference in the mobility in the four industries.

Solution Summary: The author states whether there is a difference in mobility in the four industries. The test statistic H follows the chi-square distribution with degrees of freedom.

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