The General Electric service department believes that the median time for a service call should be 30 or fewer minutes.To test this,the following random sample of service times was collected: Given that the managers do not wish to make the assumption that the population is normally distributed,the test statistic for the Wilcoxon signed rank sum test is:
A)W = 43.0
B)W = 27.0
C)W = 18.0
D)None of the above

Question

The General Electric service department believes that the median time for a service call should be 30 or fewer minutes.To test this,the following random sample of service times was collected:  Given that the managers do not wish to make the assumption that the population is normally distributed,the test statistic for the Wilcoxon signed rank sum test is:
A)W = 43.0 
B)W = 27.0 
C)W = 18.0 
D)None of the above

Quizplus · Accepted Answer

Since the population distribution is not assumed to be normal, we need to use a non-parametric test like the Wilcoxon signed-rank test. To calculate the test statistic, we need to first rank the differences between the sample and the hypothesized population median. The differences are -10, -9, -5, -3, 0, 1, 5, 6, and 7. Then we take the absolute value of the ranks and sum up the ranks corresponding to the positive differences. We get W = 27.0. Therefore, the answer is B.

The General Electric Service Department Believes That the Median Time