Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the married group.What is the standard deviation of W under the null hypothesis that the two distributions are the same?
A)4.56
B)4.79
C)22.9
D)38.67

Question

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained.  The data are to be analyzed using the Wilcoxon rank sum test.Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the married group.What is the standard deviation of W under the null hypothesis that the two distributions are the same?
A)4.56 
B)4.79 
C)22.9 
D)38.67

Quizplus · Accepted Answer

To calculate the standard deviation of W, we need to use the following formula:
SD(W) = sqrt[(n1n2/12) * [(n1+n2+1) - sum(Ti)]]
where n1 and n2 are the sample sizes of the two groups, Ti is the sum of the ranks for each group, and the sum is taken over all common values of the ranks.

In this case, n1 = 22 (number of singles) and n2 = 28 (number of married people). The sum of the ranks for the married group is W = 300, and the sum of the ranks for the single group is T = (22/2)*(22+1) - W = 253. Therefore, SD(W) = sqrt[(22*28/12) * [(22+28+1) - (300+253)]] = 4.79.

Therefore, the best choice is B.

Does Income Increase When You Get Married? to Investigate This,a