In telephone interviews with a random sample of 1100 adults nationwide conducted by the American Research Group, shoppers said they were planning to spend an average of $976 for gifts this holiday season.
a. If the standard deviation of planned spending for the sample was $180, show the 95% confidence interval estimate of the average planned spending for the population of shoppers represented by the sample.
b. Suppose you wanted to reduce the margin of error in the interval in part a by 20% without sacrificing the 95% confidence level. How big a sample would be required?