8.41 High-income households on a mailing list

Land's Beginning sells merchandise through the mail. It is considering buying a list of addresses from a magazine. The magazine claims that at least 30% of its subscribers have high incomes (that is, household income in excess of $120,000). Land's Beginning would like to estimate the proportion of high-income people on the list. Verifying income is difficult, but another company offers this service. Land's Beginning will pay to verify the incomes of an SRS of people on the magazine's list. They would like the margin of error of the 95% confidence interval for the proportion to be 0.04 or less. Use the guessed value to find the required sample size.