A economist wants to estimate the proportion of households with stale (overdue) debts. He plans to select a random sample of n households, compute the sample proportion of households with stale debts, and use it an an estimate of the corresponding population proportion.

(a) What sample size n should he use to have a margin of error no more than 3% at the confidence level 95%?

(b) Suppose he has found out that in a sample of 1000 households, 150 had overdue debts. Construct 95% and 99% confidence intervals for the population proportion.

(c) Suppose after analyzing the sample from (b), the economist provides a confidence interval p = 15% 1.86%. What is the confidence level of this interval?

(d) If the true value of the population proportion of households with stale debts is 18%, sketch the approximate distribution of the sample proportion and indicate on it the value of the sample proportion obtained in (b).