Refer to Exercise 52.

a. Construct and interpret a 95% confidence interval for the true proportion p of all first-year students at the university who would identify being very well-off as an important personal goal. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) provides more information than the test in Exercise 52.

Exercise 52.

In a recent year, 73% of first-year college students responding to a national survey identified “being very well-off financially” as an important personal goal. A state university finds that 132 of an SRS of 200 of its first-year students say that this goal is important. Is there convincing evidence at the α = 0.05 significance level that the proportion of all first-year students at this university who think being very well-off is important differs from the national value of 73%?