Back to campus again. The ACT, Inc., study described in given Exercise 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.

Exercise :
Back to campus. In 2004 ACT, Inc., reported that 74% of 1644 randomly selected college freshmen returned to college the next year. Estimate the national freshman-tosophomore retention rate.

a) Verify that the conditions are met.

b) Construct a 98% confidence interval.

c) Interpret your interval.

d) Explain what 98% confidence means in this context.