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,W can be assumed to follow a 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,W can be assumed to follow a 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

When both sample sizes are at least 10, the assumption can be made that the Wilcoxon rank-sum test statistic W follows a normal distribution 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. 
Plugging in the values given in the question, we get:
Mean = (20*25)/2 = 500
Standard deviation = sqrt(20*25*(20+25+1)/12) = 73.616
Therefore, the correct answer is B) 8100 and 434.74.

A Fund Manager Wants to Know If the Annual Rate