21. An auditor is designing a sampling plan using mean per unit estimation to te

Question

21. An auditor is designing a sampling plan using mean per unit estimation to test accounts receivable with 8,000 accounts and a recorded balance of S3,000,000. He is willing to accept a tolerable error of $80,000 although he expects the error to be only $25,000. Using a pilot sample, the auditor has estimated that the standard deviation will be $100. If the auditor has established a risk of incorrect acceptance of 5% and a risk of incorrect rejection of 10%, what will be the size of the sample? (a) 1,089. (b) 666 (c) 744 (d) 455.

Explanation / Answer

AQL = 25000/3000000 = 0.833%

LTPD = 80000/3000000 = 2.67%

LTPD / AQL = 2.67%/0.833% = 3.2

Type I error (alpha) = 10% (incorrect rejection)

Type II error (beta) = 5% (incorrect acceptance)

We look for LTPD/AQL = 3.2 in the sampling plan table

The corresponding value of c = 7 and n*LTPD = 12.133

n = 12.133/LTPD = 12.133/2.67% = 455

ANSWER: (d) 455

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