For this simulation, you are asked to calculate the last three amounts in the table. My becker book has the following two formulas though:
Sampling interval = Tolerable misstatement/ reliability factor
Sampling size = book value of population/sampling interval
Are there just two ways to find the size and interval?
You have decided to use Probability Proportional to Size (PPS) sampling, sometimes called dollar-unit sampling, in the audit of a client’s accounts receivable balances. Few, if any, errors of account balance overstatement are expected. You plan to use the provided PPS sampling table:
Reliability Factors for Errors of Overstatement
Overstatement Errors Risk of Incorrect Acceptance
1% 5% 10% 15% 20%
0 4.61 3.00 2.31 1.90 1.61
1 6.64 4.75 3.89 3.38 3.00
2 8.41 6.30 5.33 4.72 4.28
3 10.05 7.76 6.69 6.02 5.52
4 11.61 9.16 8.00 7.27 6.73
Given the following information, calculate the sampling interval and the sample size you should use.
Tolerable error $15,000
Risk of incorrect acceptance 5%
Number of errors allowed 0
Recorded amount of accounts receivable $300,000
Reliability factors for errors of overstatement 3.00
Sampling Interval $5,000
Sample Size 60
The reliability factor is taken from the provided chart, using the 5% Risk of Incorrect Acceptance, and no overstatement errors, as provided in rows 2 and 3 of this problem.
The reliability factor uses the chart information on the PPS sampling table. The reliability factor quantifies the auditor’s desired risk of incorrect acceptance based on the number of overstatement misstatements. The problem states that the number of errors allowed (or number of overstatement misstatements) is zero; this is the row always used to obtain the reliability factor for determining sample size.
The auditor must determine the sample size in advance to use PPS. The sample size is based on this formula:
Population book value x Reliability factor
Tolerable error – Expected misstatement = $300,000 x 3.00
$15,000 – 0
= $900,000
$15,000
= 60
In PPS, the sampling unit is based on dollars, not individual items or accounts. The auditors must calculate a sampling interval in order to choose the items to test. The formula for the sampling interval is:
Population book value
Sample size = $300,000
60
= $5,000
After choosing a random starting dollar value, the auditor would examine the account that contains every $5,000 from the starting point.
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