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. To determine whether the median return of growth funds is larger than the median return of value funds, the competing hypotheses are ________. A) H₀: m₁ - m₂ ≥ 0; H_A: m₁ - m₂ 0 C) H₀: m₁ - m₂ ≠ 0; H_A: m₁ - m₂ = 0 D) H₀: m₁ - m₂ = 0; H_A: m₁ - m₂ ≠ 0

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. To determine whether the median return of growth funds is larger than the median return of value funds, the competing hypotheses are ________. A) H₀: m₁ - m₂ ≥ 0; H_A: m₁ - m₂ < 0 B) H₀: m₁ - m₂ ≤ 0; H_A: m₁ - m₂ > 0 C) H₀: m₁ - m₂ ≠ 0; H_A: m₁ - m₂ = 0 D) H₀: m₁ - m₂ = 0; H_A: m₁ - m₂ ≠ 0

Quizplus · Accepted Answer

The competing hypotheses for the Wilcoxon rank-sum test are always in the form of one-sided inequality. In this case, we want to test if the median return of growth funds is larger than the median return of value funds, so the null hypothesis should assume that the difference between the two medians is less than or equal to zero (mGrowth - mValue ≤ 0), and the alternative hypothesis should assume that the difference is greater than zero (mGrowth - mValue > 0). Therefore, the correct choice is B.

A Fund Manager Wants to Know If the Annual Rate