An NBA executive says that players who substitute as the sixth, seventh and eighth positions for the games starting five players have a median playing time of 24 minutes. A random sample of 25 substitutes (6, 7 or 8) produces 20 non-zero differences in a Wilcoxon signed rank test and a W (R+) equal to 146. The alternate hypothesis is m 24 minutes. Assume the population is symmetrically distributed. The computed test statistic in this situation equals:
A)146.
B)24.
C)25.
D)1.53.
E)41.

Question

An NBA executive says that players who substitute as the sixth, seventh and eighth positions for the games starting five players have a median playing time of 24 minutes. A random sample of 25 substitutes (6, 7 or 8) produces 20 non-zero differences in a Wilcoxon signed rank test and a W (R+) equal to 146. The alternate hypothesis is m   24 minutes. Assume the population is symmetrically distributed. The computed test statistic in this situation equals:
A)146.
B)24.
C)25.
D)1.53.
E)41.

Quizplus · Accepted Answer

Since the alternate hypothesis is m>24 minutes, this is a one-tailed test. The sample size is n=25 and there are 20 non-zero differences, which means that the smallest five differences can be ignored. Therefore, the rank sum W (R+) is equal to the sum of the ranks of the remaining 20 values, which is 210. The expected value of W (R+) under the null hypothesis is n(n+1)/4 = 325/4. The standard deviation of W (R+) is sqrt(n(n+1)(2n+1)/24) = sqrt(426.875). The test statistic is (W (R+) - expected value of W (R+)) / standard deviation of W (R+), which equals (210 - 325/4) / sqrt(426.875) = -1.532. Therefore, the computed test statistic is 1.53, which is closest to choice D.

An NBA Executive Says That Players Who Substitute as the Sixth