A tax assessor wants to estimate the mean property tax bill for all homeowners in Madison, Wisconsin. A survey 10 years ago got a sample mean and standard deviation of $1400 and $1000.

a. How many tax records should the tax assessor randomly sample for a 95% confidence interval for the mean to have a margin of error equal to $100? What assumption does your solution make?

b. In reality, suppose that they’d now get a standard deviation equal to $1500. Using the sample size you derived in part a, without doing any calculation, explain whether the margin of error for a 95% confidence interval would be less than $100, equal to $100, or more than $100.

c. Refer to part b. Would the probability that the sample mean falls within $100 of the population mean be less than 0.95, equal to 0.95, or greater than 0.95? Explain.