Raising in-state and out-of-state tuition is supposed to reduce the number of students in state supported universities. The registrar of a university wants to estimate the proportion P of students who are paying for out-of-state tuition on the installment plan (to later be compared with in-state installment plan payers). A random sample of 80 students who live out-of-state is taken and 50 of them pay tuition on the installment plan. Find a 99-percent confidence interval for P, based on these data.