Auditors of a particular bank are interested in comparing the reported value of customer savings account balances with their own findings regarding the actual value of such assets. Rather than reviewing the records of each savings account at the bank, the auditors decide to examine a representative sample of savings account balances. The frame from which they will sample is given in the file P8_50.XLS.

a. What sample size would be required for the auditors to be approximately 95% sure that their estimate of the average savings account balance at this bank is within $100 of the true mean? Assume that their best estimate of the population standard deviation σ is $500.

b. Choose a simple random sample of the size found in part a.

c. Compute the observed sampling error based on the sample you have drawn from the population given in P8_50.XLS. How does the actual sampling error compare to the maximum probable absolute error established in part a? Explain.