In a Wilcoxon signed rank test for matched pairs with n = 32, the rank sums of the positive and negative differences are 367.5 and 160.5, respectively. The value of the standardized test statistic z is:
A) 3.764
B) 1.882
C) 1.391
D) 1.935
E) 1.986

Question

Quizplus · Accepted Answer

To find the standardized test statistic z, we use the formula:

z = (T - μT) / σT

where T is the smaller of the rank sums of the positive and negative differences (in this case, 160.5), μT is the mean of the rank sums under the null hypothesis (which is n(n+1)/4 = 16(17)/4 = 68) and σT is the standard deviation of the rank sums under the null hypothesis (which is sqrt(n(n+1)(2n+1)/24) = sqrt(32*33*65/24) ≈ 16.246).

Substituting these values, we get:

z = (160.5 - 68) / 16.246 ≈ 1.935

Therefore, the answer is D.

In a Wilcoxon Signed Rank Test for Matched Pairs with N