A Phoenix Wealth ManagementHarris Interactive survey of 1500

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 (to 4 decimals).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 (to 3 decimals).

Solution

b. Given n=1500, p=0.31
a=0.05,|Z(0.025)|=1.96 (check standard normal table)

So 95% CI is
p±Z*[p*(1-p)/n]

--> 0.31±1.96*sqrt(0.31*(1-0.31)/1500)

--> ( 0.2865946, 0.3334054)