Chapter 8: Problem 43
A Phoenix Wealth Management/Harris Interactive survey of 1500 individuals with net worth of \(\$ 1\) million or more provided a variety of statistics on wealthy people (Business Week, September 22,2003 ). The previous three-year period had been bad for the stock market, which motivated some of the questions asked. a. The survey reported that \(53 \%\) of the respondents lost \(25 \%\) or more of their portfolio value over the past three years. Develop a \(95 \%\) confidence interval for the proportion of wealthy people who lost \(25 \%\) or more of their portfolio value over the past three years. b. The survey reported that \(31 \%\) of the respondents feel they have to save more for retirement to make up for what they lost. Develop a \(95 \%\) confidence interval for the population proportion. c. Five percent of the respondents gave \(\$ 25,000\) or more to charity over the previous year. Develop a \(95 \%\) confidence interval for the proportion who gave \(\$ 25,000\) or more to charity. d. Compare the margin of error for the interval estimates in parts (a), (b), and (c). How is the margin of error related to \(\bar{p} ?\) When the same sample is being used to estimate a variety of proportions, which of the proportions should be used to choose the planning value \(p^{*} ?\) Why do you think \(p^{*}=.50\) is often used in these cases?