Explanation The test hypothesis is given as follows: Null hypothesis: H 0 : The durability of the paint was equal for three different conditions. Alternative hypothesis: H 1 : The durability of the paint was different for three different conditions. 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 3. Degrees of freedom for populations: k − 1 = 3 − 1 = 2 From Appendix B, Table B.7 the critical values of chi-square: Procedure: 1. In the table, first locate 2 in the first z column. 2. Locate the value of 0.01 in the second row. 3. Locate the value, by the intersection of the row and column values give the critical value. The critical value for 2 df for the 0.01 significance level is 9.210. Decision rule: If H > 9.210 , 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 ) . Where, k is the number of populations. R 1 , R 2 , ... R k is rank of samples 1, 2,… k, respectively. n 1 , n 2 , ... n k is size of samples 1, 2,… k, respectively. 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: Saltwater Rank 1 Freshwater Rank 2 Freshwater With weeds Rank 3 167

Loose Leaf for Statistical Techniques in Business and Economics

17th Edition

ISBN: 9781260152647

Author: Douglas A. Lind

Publisher: McGraw-Hill Education

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Chapter 16, Problem 23E

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State whether the durability of the paint was different for three different conditions.

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Chapter 16, Problem 22E

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Rapid drainage of floodwater is crucial to prevent damage during heavy rains. Several designs for a drainage canal were considered for a certain city. Each design was tested five times, to determine how long it took to drain the water reservoir. The following table presents the drainage times, in minutes. Channel Type Drainage Time 1 41.5 43.2 50.2 41.2 24.2 2 38.8 48.2 51.0 38.1 25.2 3 32.7 33.5 35.0 22.7 24.7 4 26.5 30.7 33.1 23.8 26.7 5 45.1 47.3 48.4 37.1 40.0 Can you conclude that there is a difference in the mean drainage times for the different channel designs? Use the =α0.01 level of significance and the ANOVA table shown below. One-way ANOVA: Drainage Source DF SS MS F P Channel 4 961.7896 240.4474 4.5623 0.0088 Error 20 1054.052 52.7026 Total 24 2015.8416 Is…

Rapid drainage of floodwater is crucial to prevent damage during heavy rains. Several designs for a drainage canal were considered for a certain city. Each design was tested five times, to determine how long it took to drain the water reservoir. The following table presents the drainage times, in minutes. Channel Type Drainage Time 1 41.4 43.4 50.0 40.9 24.1 24.2 2 38.7 48.3 51.3 38.4 25.0 29.2 3 32.7 33.8 34.4 22.6 24.5 30.0 4 26.1 31.0 33.4 23.6 26.5 31.7 5 44.7 47.0 48.6 36.9 38.9 45.9 Construct an ANOVA table. Round your answers to four decimal places. One-way ANOVA: Drainage Time Source DF SS MS F P Minutes Error Total

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Chapter 16 Solutions

Loose Leaf for Statistical Techniques in Business and Economics

Ch. 16 - Prob. 1SR Ch. 16 - Prob. 1E Ch. 16 - Prob. 2E Ch. 16 - Calorie Watchers has low-calorie breakfasts,...Ch. 16 - Prob. 4E Ch. 16 - Prob. 2SR Ch. 16 - Prob. 5E Ch. 16 - Prob. 6E Ch. 16 - Prob. 7E Ch. 16 - Prob. 8E

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State whether the durability of the paint was different for three different conditions.

Solution Summary: The author states that the durability of the paint was equal for three different conditions. The test statistic H follows the chi-square distribution with degrees of freedom.

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State whether the durability of the paint was different for three different conditions.

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