Chapter 19, Problem 26E

(a)

To determine

To explain 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.

Answer to Problem 26E

It is narrower.

Explanation of Solution

It is given in the question that it is reported that $74\%\text{ of 1644}$ randomly selected college freshmen returned to college the next year. The study was stratified by type of college, public or private. The retention rates were $\text{71}\text{.9\% among 505}$ students enrolled in public colleges and $\text{74}\text{.9\% among 1139}$ students enrolled in private colleges. Thus, the $95\%$ confidence interval for the true national retention rate in private colleges be narrower than the $95\%$ confidence interval for the retention rate in public colleges because the confidence interval will be smaller as the sample size for private colleges is much larger than the sample size for public colleges.

(b)

To determine

To explain do you expect this second poll’s overall margin of error to be larger or smaller than the Experian/Gallup’s poll.

Answer to Problem 26E

It is smaller.

Explanation of Solution

It is given in the question that it is reported that $74\%\text{ of 1644}$ randomly selected college freshmen returned to college the next year. The study was stratified by type of college, public or private. The retention rates were $\text{71}\text{.9\% among 505}$ students enrolled in public colleges and $\text{74}\text{.9\% among 1139}$ students enrolled in private colleges. Thus, we expect this second poll’s overall margin of error to be smaller than the Experian/Gallup’s poll because the pooled sample size would be much greater than either of the samples for private or public colleges.