Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds are greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. For the Wilcoxon signed-rank test for the matched-pairs, the competing hypotheses are ________. A) H₀: m_D = 0; H_A: m_D ≠ 0 B) H₀: m_D ≤ 0; H_A: m_D 0 C) H₀: m_D ≠ 0; H_A: m_D = 0 D) H₀: m_D ≥ 0; H_A: m_D

Question

Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds are greater than low-risk funds. The magazine records the return of high- and low-risk funds for a sample of 22 institutions. For the Wilcoxon signed-rank test, where D = high-risk return − low-risk return, the value of the test statistic is T = T⁺ = 185. For the Wilcoxon signed-rank test for the matched-pairs, the competing hypotheses are ________. A) H₀: m_D = 0; H_A: m_D ≠ 0 B) H₀: m_D ≤ 0; H_A: m_D > 0 C) H₀: m_D ≠ 0; H_A: m_D = 0 D) H₀: m_D ≥ 0; H_A: m_D < 0

Quizplus · Accepted Answer

The Wilcoxon signed-rank test for matched-pairs is used to compare the means of two related samples. In this case, the two samples are the high-risk and low-risk funds for each investment institution. The null hypothesis states that the mean difference between the two funds is equal to zero, while the alternative hypothesis states that the mean difference between the two funds is not equal to zero.

Option A is incorrect because it is missing the inequality symbol in the null hypothesis. Option C is incorrect because it is missing the inequality symbol in both the null and alternative hypotheses. Option D is incorrect because it has the wrong inequality symbol in both null and alternative hypotheses.

Option B is correct because it correctly states the null hypothesis as the mean difference being less than or equal to zero, and the alternative hypothesis as the mean difference being greater than zero. This aligns with the premise of the problem, which is to determine if high-risk funds have greater returns than low-risk funds.

Investment Institutions Usually Have Funds with Different Risk Versus Reward