When using statistical sampling to evaluate results using per-unit-sampling, may one conclude at the tested risk levels than an account is not materially misstated whenever the projected misstatement is less than the tolerable misstatement?

In the audit of Potomac Mills, the auditors wish to test the costs assigned to manufactured goods. During the year, the company has produced 2,000 production lots with a total recorded cost of $5.9 million. The auditors select a sample of 200 production lots with an aggregate book value of $600,000 and vouch the assigned costs to the supporting documentation. Their audit discloses misstatements in the cost of 52 of the 200 production lots; after adjustment for these misstatements, the audited value of the sample is $582,000.

1. Show how the auditors would compute an estimate of the total cost of production lots manufactured during the year using each of the following sampling plans. (Do not compute the allowance for sampling risk or the risk of incorrect acceptance of the estimates.)

1. Mean-per-unit estimation
2. Ratio estimation
3. Difference estimation

2. Explain why the mean-per-unit estimation results in a higher estimate of the population value than does ratio estimation in this particular instance.