The Auditors Are Using Mean-Per-Unit Sampling to Evaluate the Reasonableness

The auditors are using mean-per-unit sampling to evaluate the reasonableness of the book value of the accounts receivable of Smith, Inc. Smith has 10,000 receivable accounts with a total book value of $800,000. The auditors estimate the population's standard deviation as being equal to $25. After examining the overall audit plan, the auditors believe that the account's tolerable misstatement is $40,000, and that a risk of incorrect rejection of .10 (risk coefficient = 1.64) and a risk of incorrect acceptance of .15 (risk coefficient = 1.04) should be used.
Required:
a. Calculate the required sample size.
Now ignore your sample size calculation in part "a," and assume that your answer was a sample size of 289 (the square root of 289 is 17) and that you obtained the following results:
Average audited value of items in sample: $76
Average book value of items in sample: $78
Standard Deviation in the sample (audited values): $24
Standard Deviation in the sample (book values): $26
b. Using mean-per-unit sampling, calculate the projected misstatement for the population.
c. Using mean-per-unit sampling, calculate the adjusted allowance for sampling risk and use it to form a statistical conclusion concerning the book value of the population ($800,000). That is, calculate an interval and either "accept" or "reject" the client's book value.