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

Bryson Barrett · Accepted Answer

Final Answer : D, Explanation :  To find the standardized test statistic z, we use the formula:z = (T - μT) / σTwhere 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 ≈ 1.935Therefore, the answer is D.

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

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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) 3.764B) 1.882C) 1.391D) 1.935E) 1.986

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Learning Objectives

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Related questions

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