Chapter 13, Problem 33SE

College Students and Credit Card Debt In exercise 13.24 you compared credit card debts for college men and women using the Mann-Whitney test to compare medians. We’ll use the same data again, but this time you will apply a randomization test to determine whether men and women in college have different median credit card debts. There were 19 men and 18 women in this data set. As part of the randomization test, the credit card debts were randomly assigned the label “man” or “woman,” and the difference of the medians (men minus women) was calculated and recorded. This was repeated 1000 times. Figure A shows a histogram of the resulting differences of medians, and Figure B shows the resampling output.

a. Why are medians a better choice than means for comparing typical debts of men and women? Refer to the histograms given in Exercise 13.24.

b. The sample medians were $1250 for men and $725 for women, so the difference of men minus women was $525. This value is indicated with a red vertical line in the histogram. Is the observed difference unusually large? Explain.

c. The proportion of differences in the histogram that were greater than or equal to $525 is 0.245, as shown in Figure

b. Our alternative hypothesis, that the medians are different, requires a two-sided test. However, with a significance level of 0.05, and knowing that the two-sided $p$ -value must be bigger than the one-sided value of 0.245, will we reject the null hypothesis? Explain.