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: $76.50Average book value of items in sample: $78Standard Deviation in the sample (audited values): $24Standard Deviation in the sample (book values): $26b. 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.
What will be an ideal response?
a. The required sample size is calculated by:
| Sample Size |  ? |
 ? | |
 ? | |
| = 281 accounts |
| Estimated total audited value | = | (Mean of audited values) × (Number of accounts) |
| Estimated total audited value | = | ($76.50) × (10,000 accounts) |
| = | $765,000 |
| Projected misstatement | = | Estimated total audited value ? Book value of population |
| = | $800,000 ? 765,000 | |
| = | $35,000 overstatement |
| Allow. Sampling Risk |  ? |
 ? | |
| = $25,318 |
| Confidence Interval | = | Projected misstatement ± Allowance for Sampling Risk |
| = | $35,000 ± 25,318 | |
| = | ($9,682 to $60,318) |
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