Sampling for attributes is often used to allow an auditor to reach a conclusion

Question

Sampling for attributes is often used to allow an auditor to reach a conclusion concerning a rate of occurrence in a population.
A common use in auditing is to test the rate of deviation from a prescribed internal control
procedure to obtain support for a planned level of control risk.
Required
When an auditor samples for attributes, identify the factors that should influence the
auditor's judgment concerning the determination of


1. Acceptable level of risk of assessing control risk too low,
2. Tolerable deviation rate, and
3. Expected population deviation rate.

State the effect on sample size of an increase in each of the following factors, assuming all other factors are held constant:


1. Acceptable level of risk of assessing control risk too low,
2. Tolerable deviation rate, and
3. Expected population deviation rate.

Assuming nonstatistical sampling is used, evaluate the sample results of a test for
attributes if authorizations are found missing on 7 check requests out of a sample of 100
tested. The population consists of 2,500 check requests, the tolerable deviation rate is 8
percent, and the risk of assessing control risk too low should be held to a low level.
How may the use of statistical sampling assist the auditor in evaluating the sample results described in (c), above?

Explanation / Answer

Solution:

Using the sample evaluation table for a 10 percent risk of assessing control risk too low yields a computed upper limit of 10.8 percent; while lower than the computed upper limit determined for a 5 percent risk of assessing control risk too low (12.5 percent), this computed upper limit still exceeds the tolerable deviation rate of 6 percent. As a result, Joan would still conclude that the control is not functioning effectively.

Sample deviation rate = 6 ¸ 60 = 10 percent

CUL = 18.8 percent

Allowance for sampling risk = 18.8 percent – 10 percent = 8.8 percent

Because the computed upper limit (12.5 percent) exceeds the tolerable deviation rate (6 percent), Joan would conclude that the control is not functioning effectively. At this point, she could either reduce her planned level of reliance on internal control or expand the sample to examine a larger number of controls.

Sample deviation rate = 6 ¸ 60 = 10 percent

CUL = 16.9 percent

Allowance for sampling risk = 16.9 percent – 10 percent = 6.9 percent

The AICPA sample evaluation tables show, however, that none of these three sample outcomes provides adequate assurance that the population deviation rate is below 5 percent. The other sample outcome (Sample B in Case 1 and Sample A in Case 2 and 3) does provide the desired assurance at a 95 percent confidence level (5 percent risk of assessing control risk too low). Thus reliance on the representativeness of the sample outcomes could lead one to choose the weaker evidence in these cases.

Notice that the correct choice in Cases 1, 2, and 3 is the larger sample. It might be tempting to conclude that this will always be true (that is, larger samples are always superior to smaller samples). But this simplification will not always work either. Consider Cases 4 and 5. The correct answers are the smaller samples (although neither sample provides desired assurance in Case 5). Interestingly, use of the representativeness heuristic (i.e., focusing on the smaller deviation rates) would lead to the correct choices in these two instances, but would result in incorrect choices in the first three pairs of sample outcomes. This illustrates that while use of simplifying heuristics can lead to good decisions, it can also lead the decision maker into making sub optimal decisions.

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