Final answer:
The audit team compares a conservative estimate of the deviation rate to the desired confidence level, which involves known information about the sample distribution, standard deviation, and size. Replication of the sample aids in accuracy and reducing variability due to chance. Approximately 90 percent of confidence intervals from repeated samples would contain the true population mean if normally distributed.
Step-by-step explanation:
When using sampling in the study of internal control, the audit team would compare a conservative estimate of the rate of deviation to the desired confidence level. This involves understanding the information that is known about the distribution, such as any known standard deviation, and details about the sample and its size. A conservative estimate is important to ensure that the risk of concluding that the rate of deviation is acceptable when it is not, is minimized.
For accurate estimation, the standard deviation used must be suitable for the parameter being estimated, commonly referred to as the standard deviation of the sample means. This is because rules of thumb on sufficient sample sizes, replication, and controls strongly rely on the assumptions regarding the underlying distribution of the observations and the accuracy of the estimation. Replication is key for reducing the chance that random events will impact study results.
If multiple samples were taken, approximately 90 percent of the confidence intervals calculated from those samples would contain the true population mean, assuming that the underlying population is normally distributed. This statement reflects the chosen confidence level, often used when performing statistical analyses in an audit context.