46. ACT, Inc., again. The ACT, Inc. study described in Exercise 44 was actually stratified by type of college—

public or private. The retention rates were 71.9% among 505 students enrolled in public colleges and 74.9% among 1139 students enrolled in private colleges.

a) Will the 95% confidence interval for the true national retention rate in private colleges be wider or narrower than the 95% confidence interval for the retention rate in public colleges? Explain.

b) Find the 95% confidence interval for the public college retention rate.

c) Should a public college whose retention rate is 75%

proclaim that they do a better job than other public colleges of keeping freshmen in school? Explain.