Question: A state's Department of Education reports that 12% of the high school students in that state attend private high 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.

They actually select a random sample of 450 applications, and find that 46 of those students attend private schools. Create the confidence interval.