A trading magazine wants to determine the number of hours stockbrokers work each week.In particular,the trading magazine wants to determine if the median number of hours worked per week differs from 100 hours.The magazine samples 18 traders.For the Wilcoxon signed-rank test,the value of the test statistic is T = T⁺ = 153.Using the critical value approach and α = 0.01,the appropriate conclusion is _________________________________________________________________________________. A) to reject the null hypothesis;we cannot conclude the median number of hours worked per week differs from 100 B) do not reject the null hypothesis;conclude the median number of hours worked per week differs from 100 C) do not reject the null hypothesis;we cannot conclude the median number of hours worked per week differs from 100 D) reject the null hypothesis;conclude the median number of hours worked per week differs from 100

Question

Quizplus · Accepted Answer

The Wilcoxon signed-rank test is a nonparametric test used to determine if two related samples come from the same population or not. In this case, the sample of 18 traders is being compared to a hypothetical median of 100 hours. The null hypothesis is that the median number of hours worked per week is equal to 100, while the alternative hypothesis is that it is not equal to 100.

The test statistic T is calculated as 153, and the critical value for a two-tailed test at α = 0.01 with 18 observations is 28. Since T > critical value, we reject the null hypothesis and conclude that the median number of hours worked per week differs from 100. Therefore, the appropriate answer is D: reject the null hypothesis; conclude the median number of hours worked per week differs from 100.

A Trading Magazine Wants to Determine the Number of Hours