Perform a Wilcoxon rank-sum test on the two independent samples shown here to see if it supports a conclusion that median 1 is larger than median 2.Select the correct critical value (CV), test statistic (TS), and decision.(Use α = 0.01.) .
A) CV = 54, TS = 39, reject H₀
B) CV = 24, TS = 22, fail to reject H₀
C) CV = 54, TS = 39, fail to reject H₀
D) CV = 24, TS = 29, reject H₀

Question

Perform a Wilcoxon rank-sum test on the two independent samples shown here to see if it supports a conclusion that median 1 is larger than median 2.Select the correct critical value (CV), test statistic (TS), and decision.(Use α = 0.01.) ​  .
A) CV = 54, TS = 39, reject H₀ 
B) CV = 24, TS = 22, fail to reject H₀ 
C) CV = 54, TS = 39, fail to reject H₀ 
D) CV = 24, TS = 29, reject H₀

Quizplus · Accepted Answer

Since α = 0.01, we need to find the critical value (CV) from the Wilcoxon rank-sum table for a two-tailed test at α/2 = 0.005 with sample sizes n1 = 10 and n2 = 14. The CV is 54.

The test statistic (TS) is the sum of ranks for the smaller sample size, which in this case is Sample 1. The sum of ranks for Sample 1 is 39.

Since the TS (39) is less than the CV (54), we fail to reject the null hypothesis, which states that there is no significant difference between the medians. Therefore, we cannot conclude that median 1 is larger than median 2 at the 1% significance level.

Perform a Wilcoxon Rank-Sum Test on the Two Independent Samples