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Sampling to test the reasonableness of the recorded book value

You decide to use statistical sampling to test the reasonableness of the recorded book value of the Key West Company's accounts receivable. Because the company's internal control procedures over accounts receivable have been evaluated by you as excellent and you believe few misstatements will be found, you decide to use probability proportional- to-size sampling. The company has 4,000 customer accounts with a total book value of $3,000,000. You decide $150,000 is the maximum tolerable misstatement and anticipate that there may be $30,000 of misstatement in the population. You wish to limit the risk of incorrect acceptance to 10%. It is your intention to seek positive confirmation of accounts included in your sample and to apply alternative procedures to accounts for which no reply is received.
a. Compute the sample size.
b. Compute the sampling interval.
c. Assume the following misstatements were found in the sample:
1 $800 $0
2 1,500 1,350
3 13,000 0
4 15,000 14,250
1. Projected misstatement.
2. Allowance for sampling risk.
3. Upper misstatement limit.
d. State your conclusion based on the results in (c).

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Statistical Sampling

Calculation of Sample Size:
Sample size =
Total no. of Customers Account = 4000
Total Book Value (BV) = $3000000
Tolerable Misstatement (TM) = $150000
Anticipate Misstatement (AM) = $30000
Reliability Factor for the 10% risk of incorrect acceptance (RF) = 2.31 (Exhibit-1)
Expansion Factor for AM at 10% risk of incorrect acceptance (EF) = 1.5 (Exhibit-2)
Sample Size = = 66
So, the sample size for the statistical sampling will be 66.
Calculation of Sampling Interval:
Sampling interval =
Book Value of account receivables = $3000000
Sampling Interval = = $45455
So, the sampling interval for statistical sampling will be $45455.
Calculation of Projected misstatement:
Project misstatement = (Tainting percentage × Sampling interval)
Tainting Percentage = (Book value - Audit value) ÷ Book value
(Boynton & Johnson, 2009).
Sampling Interval = 45455
Calculation of projected misstatement for each sample is as follow-
Sample Book Value Audit Value Misstatement Taint (%) Sampling ...

Solution Summary

Statistical sampling to test the reasonableness of the recorded book values are examined.