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: $76.50
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 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.