A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test. Because both sample sizes are at least 10, the sampling distribution of W can be approximated by the normal distribution with a mean and standard deviation of ________, respectively.
A) 434.74 and 8100
B) 8100 and 434.74
C) 8100 and 189000
D) 189000 and 8100

Question

A fund manager wants to know if the annual rate of return is greater for growth stocks (sample 1) than for value stocks (sample 2). The fund manager collects data on the returns of growth and value funds. Below are the sample sizes and rank sums for the Wilcoxon rank-sum test.  Because both sample sizes are at least 10, the sampling distribution of W can be approximated by the normal distribution with a mean and standard deviation of ________, respectively.
A) 434.74 and 8100 
B) 8100 and 434.74 
C) 8100 and 189000 
D) 189000 and 8100

Quizplus · Accepted Answer

According to the Wilcoxon rank-sum test, the test statistic W is approximately normally distributed with a mean of n1n2/2 and a standard deviation of sqrt(n1n2(n1+n2+1)/12), where n1 and n2 are the sample sizes for sample 1 and sample 2, respectively. Plugging in the given sample sizes, we get a mean of 100*90/2 = 4500 and a standard deviation of sqrt(100*90*(100+90+1)/12) = 67.37. Therefore, the correct answer is B, with the mean and standard deviation listed in the correct order.

A Fund Manager Wants to Know If the Annual Rate