Final answer:
When determining sample size for a test of controls, auditors must consider the expected deviation rate, the desired confidence level, and the tolerable deviation rate along with distribution information and the characteristics of the sample and population.
Step-by-step explanation:
In determining the sample size for a test of controls, an auditor should consider the expected deviation rate, the desired confidence level, and the tolerable deviation rate. This assessment is crucial in audit planning to ensure that the test of controls will provide reasonable assurance that the control activities are operating effectively. Various statistical and non-statistical factors must be taken into account, such as the information known about the distribution, including any known standard deviation, and the characteristics of the sample and its size.
For a hypothesis test, the type of distribution and whether the standard deviation is known or unknown are important considerations. Auditors also must follow rules of thumb on sufficient sample sizes, which may depend on the underlying distribution of the observations, width of Bayesian posterior credibility intervals, or previous experiences from similar studies. The literature suggests that the sample size should be at least 30 or more, or the data should come from a normal distribution to rely on the normal test method.
To ensure the reliability of the audit's conclusions, it's essential that samples are simple random samples, and that populations have sufficient size relative to the sample—in most cases, at least 10 or 20 times larger. When dealing with rare events or when sampling variability is a concern, larger samples help minimize the differences between the actual population parameter and the sample statistic.