Problem 3. 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 71 should he use to have a margin of error no more than 3% at the condence level 95%? (b) Suppose he has found out that in a sample of 1000 households, 150 had overdue debts. Construct a 95% and 99% condence for the population proportion. (c) Suppose after analyzing the sample from (b), the economist provides a condence interval p = 15% :l: 1.86%. What is the condence 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)