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.Using the critical value approach,the appropriate conclusion is:
A)Reject the null hypothesis,conclude the median return of growth stock is greater than the median return of value stocks
B)Reject the null hypothesis,conclude the median return of value stock is greater than the median return of growth stocks
C)Reject the null hypothesis,conclude the median return of growth stock differs from the median return of value stocks
D)Reject the null hypothesis,cannot conclude the median return of growth stocks is greater than the median return of value stocks

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.Using the critical value approach,the appropriate conclusion is:
A)Reject the null hypothesis,conclude the median return of growth stock is greater than the median return of value stocks 
B)Reject the null hypothesis,conclude the median return of value stock is greater than the median return of growth stocks 
C)Reject the null hypothesis,conclude the median return of growth stock differs from the median return of value stocks 
D)Reject the null hypothesis,cannot conclude the median return of growth stocks is greater than the median return of value stocks

Quizplus · Accepted Answer

The Wilcoxon rank-sum test is a non-parametric test used to compare the median values of two independent groups. The null hypothesis for this test is that there is no difference between the medians of the two groups.

In this case, the rank sum for growth stocks is 295, and the rank sum for value stocks is 155. The sample sizes are 10 and 9, respectively.

Using the critical value approach, with alpha level of 0.05 and sample sizes of 10 and 9, the critical value is 22 (taken from the Wilcoxon rank-sum table). Since the calculated rank sum of 295 is greater than the critical value of 22, we reject the null hypothesis.

Therefore, we can conclude that the median return of growth stocks is greater than the median return of value stocks. The correct answer is A.