(Solution) - USA Today notes Mary Beth Marklein College Gender Gap Widens -(2025 Original AI-Free Solution)

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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.