Final answer:
The correct statement concerning statistical sampling in tests of controls is that there is an inverse relationship between the expected population deviation rate and the sample size. Sample size determination is not necessarily proportional to population size and an auditor considers detection risk, not the sample size, when determining tolerable deviation rate.
Step-by-step explanation:
Statistical Sampling in Tests of Controls
Regarding the correctness of statements about statistical sampling in tests of controls:
As the population size increases, the common misconception is that the sample size should increase proportionately. However, this is not accurate because sample size determination depends more on the desired level of confidence and the acceptable error margin than just the population size. For large populations, after a certain point, the additional precision gained by an increased sample size is often minimal.
Deviations from specific internal control procedures usually result in misstatements at a lower rate, which acknowledges that not all deviations will lead to material misstatements.
There is indeed an inverse relationship between expected population deviation rate and sample size. This means that the higher the expected deviation rate, the smaller the sample size needed to detect it with the same level of confidence. Conversely, if the expected deviation is low, a larger sample may be required to identify it.
When determining the tolerable deviation rate, an auditor will consider factors such as detection risk and the characteristics of the population, among others, but not directly the sample size.
Overall, statistics utilize sample observations to make inferences about a population, where the law of large numbers and the central limit theorem play critical roles in ensuring that sample means approximate the population mean as sample sizes increase.