Exhibit 20.6.A fund manager wants to know if the annual rate of return is greater for growth stocks (1)than value stocks (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. Refer to Exhibit 20.6.Since both sample sizes are at least 10,W can be assumed to follow a normal distribution with a mean and standard deviation of:
A)434.74 and 8100
B)8100 and 434.74
C)8100 and 189000
D)189000 and 8100

Question

Exhibit 20.6.A fund manager wants to know if the annual rate of return is greater for growth stocks (1)than value stocks (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.  Refer to Exhibit 20.6.Since both sample sizes are at least 10,W can be assumed to follow a normal distribution with a mean and standard deviation of:
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, W can be assumed to follow a normal distribution with a mean of n1n2/2 and a standard deviation of sqrt(n1n2(n1+n2+1)/12). Therefore, in this case, the mean is (10*12)/2=60 and the standard deviation is sqrt(10*12*23/12)=43.47. However, it is important to note that since W is a discrete variable, the normal distribution approximation may not be exact, especially when the sample sizes are small.