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. Using the critical value approach and α = 0.01,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) do not reject the null hypothesis;conclude the median return of value stock is greater than the median return of growth stocks
C) do not reject the null hypothesis;conclude the median return of growth stock differs from the median return of value stocks
D) reject the null hypothesis;we cannot conclude the median return of growth stocks is greater than the median return of value stocks

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.  Using the critical value approach and α = 0.01,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) do not reject the null hypothesis;conclude the median return of value stock is greater than the median return of growth stocks 
C) do not reject the null hypothesis;conclude the median return of growth stock differs from the median return of value stocks 
D) reject the null hypothesis;we 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 determine if two independent samples come from populations with the same median. In this case, we have two samples (growth stocks and value stocks), and we want to determine if their annual rate of return is different.

The critical value approach involves comparing the calculated test statistic (here, the rank sum for growth stocks) with the critical value from a table. The critical value depends on the sample sizes and the level of significance (here, α = 0.01). In our case, the critical value for a two-tailed test with sample sizes of 20 and 25 is 128.

The rank sum for growth stocks in the table is 341, which is greater than the critical value of 128. Therefore, we reject the null hypothesis and conclude that the median return of growth stocks is greater than the median return of value stocks. Hence, the appropriate conclusion is A.

A Fund Manager Wants to Know If the Annual Rate