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.

a) They select a random sample of 500 applications and find that 52 of those students attend private schools. Check the conditions required for inference. (3 marks)

b) Create the 95% confidence interval. (6 marks)

c) Interpret the confidence interval in this context. (3 marks)

d) 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. (2 marks)