Aaliyah is about to graduate from Arcadia. She plans to move to either San Francisco or Denver and search for work. Recent data reports⁴that average starting salaries for college graduates are $48,900 in San Francisco and $40,900 in Denver. Suppose these data were based on 100 recent graduates in each city where the population standard deviation is $16,000 in San Francisco and $14,500 in Denver. For social reasons, Aaliyah is also interested in the percent of the population who are in their twenties. The same report states that 20% of the population are in their twenty in San Francisco; the corresponding percentage in Denver is 22%.

c. Conduct a hypothesis test at the 5% significance level to determine whether the proportion of the population in their twenties differs in these two cities.

d.Construct a confidence interval appropriate for the hypothesis test in part (c). Do the results support your findings in part (c)? Explain your thinking.