USA Today notes (Mary Beth Marklein, “College Gender Gap Widens: 57% Are Women”) that there are more men than women ages 18–24 in the United States—15 million versus 14.2 million. The male/female ratio in colleges today is 42.6/57.4.

However, there is a discrepancy in the percentage of males dependent on their parents’ income. The file entitled Diversity contains the gender of undergrads

(18–24) whose parents’ income is in two categories:

(1) low income—less than $30,000, and (2) upper income—$70,000 or more.

a. Determine if the sample sizes are large enough so that the sampling distribution of the difference between the sample proportions of male undergraduates in the two income categories can be approximated by a normal distribution.

b. Perform a test of hypothesis to determine that the proportion of male undergraduates in the upper income category is more than 1% greater than that of the low income category. Use a significance level of 0.01.

c. Calculate the difference between the two sample proportions. Given the magnitude of this difference, explain the results of part b.