Final answer:
The correct statement is that the auditor should consider the tolerable deviation rate when determining the sample size for testing controls. Factors such as the estimated rate of deviation and the allowable risk of assessing control risk too low significantly affect the sample size, while the population size generally has a lesser effect, especially for large populations.
Step-by-step explanation:
When testing controls in statistical sampling, auditors must carefully determine the appropriate sample size for the audit to be reliable. The correct statement out of the options provided is: the auditor should consider the tolerable deviation rate from the controls being tested in determining sample size. This means that the auditor should indeed account for the maximum error rate that could be accepted without altering the conclusion about the control effectiveness.
As for other factors affecting the sample size, it is noteworthy that, contrary to one of the options provided, as the estimated rate of deviation decreases, the auditor may actually decrease the planned sample size since a lower deviation rate suggests better control effectiveness. Moreover, the allowable risk of assessing control risk too low (also known as the risk of overreliance) does have a significant effect on the sample size as increasing this risk allows for a smaller sample size.
Additionally, while the population size can affect the sample size needed, it is usually the least impactful factor, especially when the population is large, because the sample size does not increase proportionally with the population size.
In the context of larger samples, they are preferred because they provide a better representation of the population and reduce the sampling variability, consequently increasing the reliability of the statistical findings. This supports the fact that larger samples tend to produce more accurate estimates of the population parameters.