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. The previous three-year period has 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 =.50 is often used in these cases?
The solution provides a detailed explanation of the determination of Margin of Error and Confidence interval.