An online survey by ShareBuilder, a retirement plan provider, and Harris Interactive reported that 60% of female business owners are not confident they are saving enough for retirement (SmallBiz, winter 2006). Suppose we would like to do a follow-up study to determine how much female business owners are saving each year toward retirement and want to use $100 as the desired margin of error for an interval estimate of the population mean. Use $1,100 as a planning value for the standard deviation and recommend a sample size for each of the following situations.
a. A 90% confidence interval is desired for the mean amount saved.
b. A 95% confidence interval is desired for the mean amount saved.
c. A 99% confidence interval is desired for the mean amount saved.
d. When the desired margin of error is set, what happens to the sample size as the confidence level is increased? Would you recommend using a 99% confidence interval in this case? Discuss.