Certified Internal Auditor (CIA) Practice Test

When an auditor estimates the total value of inventory using the mean-per-unit method, and uses a precision of +-4% with 90% confidence, what percentage chance does the auditor have that the actual total is less than US $768,000 or more than US $832,000?

1. 10%

2. 4%

3. 14%

4. 6%

The correct answer is: 4%

Using the mean-per-unit method with specified precision and confidence levels allows the auditor to estimate the total value of inventory with a quantitative measure of uncertainty. When the auditor sets a precision of ±4% with a 90% confidence level, this means that there is a 90% probability that the actual value of the inventory lies within the range defined by the estimated total, specifically 4% above or below this estimate. Given the estimated total, the calculation for the upper and lower bounds can be performed. If the estimate of the total inventory is, for instance, around $800,000, then ±4% of that amount would lead to a lower bound of approximately $768,000 and an upper bound of about $832,000. The 90% confidence level implies that there is a 10% probability that the actual total will lie outside these bounds. This suggests that there is a 5% chance that the total is less than $768,000 and another 5% chance that it is more than $832,000. Thus, the combined probability of the total being outside this range—either below $768,000 or above $832,000—is 5% + 5%, equaling 10%.