A Wilcoxon rank sum test for comparing two populations involves two independent samples of sizes 15 and 20. The nonstandardized test statistic (that is, the rank sum) is T = 210. Under these circumstances, what is the value of the standardized test statistic z?
A) 14.0
B) 10.5
C) 6.0
D) -2.0

Question

Quizplus · Accepted Answer

The standardized test statistic z for the Wilcoxon rank sum test is calculated using the formula: z = (T - mean(T)) / standard deviation(T). For two samples of sizes 15 and 20, the mean(T) = n1(n1+n2+1)/2 = 15(36)/2 = 270 and the standard deviation(T) = sqrt(n1*n2(n1+n2+1)/12) = sqrt(15*20*36/12) = sqrt(900) = 30. Thus, z = (210 - 270) / 30 = -2.0.

A Wilcoxon Rank Sum Test for Comparing Two Populations Involves