Question

The size of a given sample is jointly a result of characteristics of the population of interest and decisions made by the internal auditor. Everything else being equal, sample size will?

1) Increase if the internal auditor decides to accept more risk of incorrectly concluding that controls are effective when they are in fact ineffective.
2) Double if the internal auditor finds that the variance of the population is twice as large as was indicated in the pilot sample.
3) Decrease if the internal auditor increases the tolerable rate of deviation.
4) Increase as sampling risk increases.

Answer 1

Increasing the sample size is often necessary when an auditor faces higher sampling risks to maintain the statistical validity and reliability of their findings.

Step-by-step explanation:

Sample size and its relationship to sampling risk form a fundamental concept in statistics and are particularly relevant in the field of auditing. When an internal auditor determines the size of a sample, they must consider the characteristic of the population of interest as well as their own decisions regarding acceptable levels of uncertainty.

As sampling risk increases, the necessity for a larger sample size typically increases as well. More specifically, if an auditor wishes to achieve a higher confidence level or reduce the error bound in their conclusions, they will need to consider expanding their sample size. With a larger sample size, the law of large numbers suggests that the sample mean will more likely approximate the population mean, thereby reducing the sampling error.

This decision facilitates a more reliable estimate of the population parameter of interest. Therefore, with everything else held constant, an increase in sampling risk translates into an increased requirement for the sample size in order to maintain the statistical validity and reliability of the audit findings.