Certified Internal Auditor (CIA) Practice Test

When can random numbers be used to select a sample?

1. When each item can be assigned to a specific stratum.

2. When each item is independent of outside influence.

3. When each item can be identified with a unique number.

4. When each item is within plus or minus three standard deviations of the population mean.

The correct answer is: When each item can be identified with a unique number.

Random numbers can be effectively used to select a sample when each item can be identified with a unique number. This identification allows for straightforward selection processes where each item within the population has an equal chance of being chosen. The process of assigning unique identifiers helps in ensuring that the sampling is random and not biased, as it allows for the application of techniques that can generate random selections from a finite population. In the context of sampling, having unique identifiers is vital because it facilitates the use of random number generators or tables to select items without the risk of duplication or omission. This principle underpins much of statistical sampling methodology, ensuring that each element has a fair representation in the sample drawn. The other options relate to different sampling methods or conditions and do not directly support the concept of random number sampling in the same way. Stratum identification, independence from outside influences, and standard deviation parameters are important considerations in certain contexts but do not inherently validate the use of random number selection on their own. This makes the option regarding unique identification the most relevant to random sampling criteria.