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 unknown and the sample size is less than 30, we use the Wilcoxon signed rank sum test. We first rank the absolute differences between the sample values and the hypothesized value (30), then calculate the sum of positive ranks (W+) and negative ranks (W-), and take the smaller of the two values as the test statistic (W). In this case, the positive ranks are 13, 18, and 19, and the negative ranks are 1, 2, 3, 4, 5, and 6. The sum of positive ranks is W+ = 13 + 18 + 19 = 50, and the sum of negative ranks is W- = 1 + 2 + 3 + 4 + 5 + 6 = 21. Therefore, the test statistic is W = min(W+, W-) = 21.

The General Electric Service Department Believes That the Median Time