Question: A survey of first-time home buyers found that the mean annual household income was $62,000. Assume the survey used a sample of 100 first-time home buyers and assume that the population standard deviation is $19,700.

(a) What is the 95% confidence interval for the population mean annual household income for first-time home buyers?

(b) Without redoing your calculations, how would the width of the confidence interval change if the sample size was increased to 400 (with the rest of the data remaining the same)?