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.If T is assumed to follow a normal distribution,the value of the test statistic is _____. A) 153 B) 2.94 C) 0.128 D) −2.94

Question

Quizplus · Accepted Answer

The Wilcoxon signed-rank test is a non-parametric test, meaning it does not make any assumptions about the distribution of the data. However, in order to use the test statistic value to determine whether or not to reject the null hypothesis (that the median number of hours worked per week is 100), we need to assume that the test statistic follows a normal distribution.

To obtain the value of the test statistic under a normal distribution, we use the following formula:

z = (T - μT) / σT

where T is the value of the test statistic under the Wilcoxon signed-rank test, μT is the mean of the test statistic under the null hypothesis (which is 0), and σT is the standard deviation of the test statistic under the null hypothesis. The standard deviation can be approximated using the following formula:

σT = sqrt[(n(n+1)(2n+1))/6]

where n is the sample size (which is 18 in this case).

Plugging in the values, we get:

z = (153 - 0) / (sqrt[(18*19*37)/6]) = 2.94

Therefore, the answer is B.

A Trading Magazine Wants to Determine the Number of Hours