Investment institutions usually have funds with different risk versus reward prospectuses. A trading magazine wants to determine if the returns of high-risk funds is 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. Using the p-value approach and α = 0.10, the appropriate conclusion is ________. A) to reject the null hypothesis; we can conclude the median difference of the returns is greater than zero B) to reject the null hypothesis; we cannot conclude the median difference of the returns is greater than zero C) do not reject the null hypothesis; we cannot conclude the median difference of the returns is greater than zero D) do not reject the null hypothesis; we can conclude the median difference of the returns is greater than zero

Question

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The Wilcoxon signed-rank test is used to compare two related samples to determine whether their population mean ranks differ. If the test statistic (T) leads to a p-value less than the significance level (α = 0.10), we reject the null hypothesis. The statement suggests that the evidence (T = 185) is significant enough to reject the null hypothesis, implying that there is a statistically significant difference in the median returns of high-risk and low-risk funds, favoring the conclusion that the median difference is greater than zero.

Investment Institutions Usually Have Funds with Different Risk Versus Reward