# Question

Bill Pei, CPA, is about to begin his audit of the accuracy of his client’s accounts receivable. Based on experience, he expects that approximately 1 percent of the client’s 40,000 accounts have errors.

The total book value of receivables is $5 million. Pei has established $390,000 as the amount of tolerable misstatement, 5 percent for the risk of incorrect acceptance, and 10 percent for the risk of incorrect rejection. The auditor estimates the standard deviation of the accounts to be $45.

a. Using mean-per-unit sampling, calculate the required sample size.

b. Now ignore part (a). Assume that as part of an attributes sampling plan using a stipulated tolerable rate of 5 percent and a risk of assessing control risk too low of 5 percent, the auditor wishes to test the receivables valuation—that is, each account will be considered as either correct or a deviation. What sample size would be required for this test?

Now ignore your (a) and (b) answers and assume that the auditor selected a random sample of 208 accounts (square root = 14.4), representing a total book value of receivables of $40,800.

He found five errors, representing a $20,300 overstatement as follows:

The standard deviation of the book value of the sample was $50, while the standard deviation of the audited values of the sample was $55.

c. Using mean-per-unit estimation, what is the projected misstatement for the population?

d. Using mean-per-unit sampling, calculate the adjusted allowance for sampling risk and use it to calculate the appropriate interval for use in deciding whether to “accept” or “reject” the population.

e. Using difference estimation, calculate the projected misstatement for the population.

f. Given the five misstatements presented earlier, what statistical conclusion may be made using attributes sampling (recall part [b] from the previous page)?

g. Assume a sampling interval of $24,038 ($5,000,000/208). Using PPS sampling, calculate:

(1) Projected misstatement.

(2) Basic precision.

(3) Incremental allowance for samplingrisk.

The total book value of receivables is $5 million. Pei has established $390,000 as the amount of tolerable misstatement, 5 percent for the risk of incorrect acceptance, and 10 percent for the risk of incorrect rejection. The auditor estimates the standard deviation of the accounts to be $45.

a. Using mean-per-unit sampling, calculate the required sample size.

b. Now ignore part (a). Assume that as part of an attributes sampling plan using a stipulated tolerable rate of 5 percent and a risk of assessing control risk too low of 5 percent, the auditor wishes to test the receivables valuation—that is, each account will be considered as either correct or a deviation. What sample size would be required for this test?

Now ignore your (a) and (b) answers and assume that the auditor selected a random sample of 208 accounts (square root = 14.4), representing a total book value of receivables of $40,800.

He found five errors, representing a $20,300 overstatement as follows:

The standard deviation of the book value of the sample was $50, while the standard deviation of the audited values of the sample was $55.

c. Using mean-per-unit estimation, what is the projected misstatement for the population?

d. Using mean-per-unit sampling, calculate the adjusted allowance for sampling risk and use it to calculate the appropriate interval for use in deciding whether to “accept” or “reject” the population.

e. Using difference estimation, calculate the projected misstatement for the population.

f. Given the five misstatements presented earlier, what statistical conclusion may be made using attributes sampling (recall part [b] from the previous page)?

g. Assume a sampling interval of $24,038 ($5,000,000/208). Using PPS sampling, calculate:

(1) Projected misstatement.

(2) Basic precision.

(3) Incremental allowance for samplingrisk.

## Answer to relevant Questions

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