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1. A state’s department of education reports that 12% of the high school students in that state attend private schools. The state university wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools.
a. The admission officers want to estimate the true percentage of private school applicants to within 4%, with 90% confidence. How many applications should they sample?
b. They actually select a random sample of 450 applications, and find that 46 of those students attend private schools. Create the 90% confidence interval and interpret it in this context.
c. Should the admissions officers conclude that the percentage of private school students in their applicant pool is lower than the statewide enrollment rate of 12%? Explain your answer.