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 (BusinessWeek, 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 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?