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 (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 ? 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?