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 value of z,the standardized value of W?
A)0.84
B)1.36
C)1.43
D)2.62

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 value of z,the standardized value of W?
A)0.84 
B)1.36 
C)1.43 
D)2.62

Quizplus · Accepted Answer

Using the Wilcoxon rank sum test, we calculate W to be 106.5 (sum of ranks assigned to the married group). Then, we calculate the expected value E(W) and the variance Var(W) under the null hypothesis that there is no difference in income between married and unmarried individuals. We get E(W) = (n1n2)/2 = (24*26)/2 = 312 and Var(W) = (n1n2(n1+n2+1))/12 = (24*26*(24+26+1))/12 = 1040. We can now calculate the standardized value of W using the formula z = (W - E(W))/sqrt(Var(W)) = (106.5-312)/sqrt(1040) = -2.21 (negative because the married group had lower incomes). However, we need to compare this value with the critical value of z at the alpha level (usually 0.05) from a standard normal distribution table. For a two-tailed test, the critical z is 1.96. Since our calculated z (-2.21) is less than the critical z (-1.96), we reject the null hypothesis and conclude that there is evidence of a difference in income between married and unmarried individuals. The answer closest to -2.21 is B) 1.36.

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