Question

Question 22 9 pts Use the Wilcoxon rank sum test on the data below to determine at the 10% significance level whether the two population locations differ. Sample 1 32 22 19 29 20 34 25 9 28 17 Sample2 29 2018 27 19 23 19 12 22 10 HO: the two population locations are the same Ha: the two population locations are different Test statistics = [Select] Critical Value = [Select ] Conclusions: [ Select]

options are

1. 90/ 90.5/91

2. 80/81/82

3. the two population locations are the same

the two population locations are different

the results are inconclusive

Answer 1

The Wilcoxon rank-sum test is to be performed on the given data at the 10% significance level whether the two population locations differ. Sample1 32 22 19 29 20 34 25 9 28 17 Sample2 29 20 18 27 19 23 19 12 22 10 The hypotheses are written as follows: H,: The two populations' locations are the same. H: The two population locations are different. Now, arrange the data in the ascending order and given the rank as follows: Original Date 32 22 19 29 20 34 25 Ranks 19 11.5 7 17.5 9.5 20 14 1 Sample Sample 1 Sample 1 Sample 1 Sample 1 Sample 1 Sample 1 Sample 1 Sample 1 Sample 1 Sample 1 Sample 2 Sample 2 Sample 2 Sample 2 Sample 2 Sample 2 Sample 2 Sample 2 Sample 2 Sample 2 9 28 17 29 20 16 4 17.5 9.5 5 18 27 15 7 13 7 19 23 19 12 22 10 3 11.5 2 Hence, The sum of the ranks of sample 1 is, W =( 19+11.5 +7+17.5+9.5+20+14+1+16+4) = 119.5

The sum of the ranks of sample 2 is, W' =( 17.5+9.5+5+15+7+13+7+3+11.5+2) = 90.5 The value of test statistic is the rank-sum value that is minimum, that is, Test statistic=min(WW') = min (119.5, 90.5) = 90.5 Thus, the value obtained is Test statistic = 90.5 The level of significance is a = 0.10 and the test is two-tailed. The sample sizes are n =10 and n =10. Using the Wilcoxon rank-sum table, the critical value is W = 82 crical Two-sided One-sided Level of significance a 0.20 0.10 0.10 0.05 n 10 6 38 35 10 7 49 45 10 8 80 56 10 9 73 87 69 82 10 10 The decision rule is the null hypothesis is rejected if Test statistics 582. Since, min (W,W') =90.5 > 82 =Writical , the null hypothesis is not rejected. Hence, there is not enough evidence to conclude that the two population locations are different. Thus, Critical value = 82 Conclusion: The two population locations are the same