The National Collegiate Athletic Association (NCAA) requires colleges to report the graduation rate of their athletes. At one large university, 69% of all students who entered in 1994 graduated within six years. Ninety-six (96) of the 152 students who entered with athletic scholarships graduated. Construct the 99% confidence interval for the proportion of athletes who graduate.

The 99% confidence interval for the proportion of athletes who graduate is (0.5309, 0.7323).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

For this problem, we have that:

99% confidence level

So , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 99% confidence interval for the proportion of athletes who graduate is (0.5309, 0.7323).