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 titled 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 under-graduates 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.