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. Given the sample size, the sampling distribution of T can be approximated by the normal distribution as the sample size is greater than 10; T can be assumed to follow the normal distribution with mean and standard deviation ________, respectively. A) 126.5 and 30.80 B) 30.80 and 126.5 C) 125.5 and 948.75 D) 30.80 and 984.75

Question

Quizplus · Accepted Answer

For the Wilcoxon signed-rank test with a sample size of 22, the mean (μ) and standard deviation (σ) of the test statistic T can be calculated using the formulas μ = n(n+1)/4 and σ = sqrt(n(n+1)(2n+1)/24), where n is the sample size. For n = 22, μ = 22(23)/4 = 126.5 and σ = sqrt(22(23)(45)/24) = 30.80.

Investment Institutions Usually Have Funds with Different Risk Versus Reward