A recent poll of 1005 U.S. adults split the sample into four age groups: ages 18-29, 30-49, 50-64, and 65+. In the youngest age group, 62% said that they thought the U.S. was ready for a woman president, as opposed to 35% who said “no, the country was not ready” (3% were undecided). The sample included 250 18- to 29-year-olds.

a) Do you expect the 95% confidence interval for the true proportion of all 18- to 29-year-olds who think the U.S. is ready for a woman president to be wider or narrower than the 95% confidence interval for the true proportion of all U.S. adults? Explain.

b) Find the 95% confidence interval for the true proportion of all 18- to 29-year-olds who believe the U.S. is ready for a woman president.