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

question 48

Essay

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.

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Definitions:

Cash Dividend

Cash distributed by a business to its owners from the earnings it has generated.

Net Amount

The remaining balance of a transaction after all deductions, including taxes and discounts, have been applied.

Long-Term Investments

Assets intended to be held for more than one year, including stocks, bonds, real estate, and other financial instruments.

Equity Securities

Financial instruments that represent ownership interests in corporations, such as stocks.