The auditor uses monetary-unit sampling (MUS) to conduct substantive tests for an account. The desired confidence level in selecting the sample is 95%, the upper misstatement limit (UML) is $11,200, and the auditor’s tolerable misstatement is $14,000. Which of the following is a true statement?

Question

BlackTom AI · Accepted Answer

We start by restating the scenario and the answer options to ensure clarity.
Question context: The auditor uses monetary-unit sampling (MUS) for substantive testing. Desired confidence level: 95%. Upper misstatement limit (UML): $11,200. Tolerable misstatement: $14,000. Options to evaluate include statements about sampling risk, probabilities, and conclusions about material misstatement.
Option 1: 'There is a 5% probability that the total misstatement exceeds the tolerable misstatement.' This describes the risk of incorrect acceptance (Type II risk) at the planned confidence level. In MUS, the standard interpretation is that the sampling risk is tied to the confidence level (here 95%), which corresponds to a 5% risk of incorrect conclusion, but this option would imply the risk directly for exceedance of tolerable misstatement, which is not precisely how MUS sampling risk is framed in this context. Moreover, the 5% pertains to the chance of not detecting misstatement beyond tolerable levels given the sampling plan, not a direct statement about the total misstatement exceeding tolerable misstatement.
Option 2: 'There is a 95% probability that the total misstatement in the account does not exceed $11,200.' This would misstate UML as a probability statement about the total misstatement staying under UML. UML is a planning parameter used to establish sample size and acceptance criteria, not a probabilistic bound on the total misstatement with that exact confidence. The confidence level of 95% refers to the sampling process, not a guaranteed probability that the total misstatement is below UML.
Option 3: 'The auditor will conclude the account is materially misstated.' This is a definitive conclusion about materiality based on the MUS sample. While MUS results influence the conclusion, there is no inherent guarantee that the sample will always lead to a conclusion of material misstatement; the conclusion depends on the measured misstatement relative to tolerable misstatement and the sampling results, followed by professional judgment. Therefore this statement is overly deterministic and not always true.
Option 4: 'The allowance for sampling risk is $2,800.' This aligns with the relationship between UML and tolerable misstatement: sampling risk allowance is the difference between tolerable misstatement and UML (Tolerable - UML = 14,000 - 11,200 = 2,800). This amount represents the amount of sampling risk one is willing to accept when the objective is to have 95% confidence that the MUS conclusions do not exceed the tolerable misstatement. In other words, if the sample yields results at or below UML, the remaining risk captured by the difference to the tolerable misstatement is accounted for as sampling risk.
A few subtle clarifications to avoid common misunderstandings:
- The 95% confidence level refers to the likelihood that the MUS sample will lead to a conclusion within the tolerable misstatement boundary, not to a 95% probability that the UML bound itself will hold across all population misstatements.
- UML is the maximum misstatement the auditor is willing to tolerate in the account balance as discovered in the MUS plan, not a guaranteed cap on the total misstatement.
- The difference between tolerable misstatement and UML represents the amount of sampling risk the auditor is intentionally accepting; it is not a statement about the actual misstatement in the population but about the risk envelope used for planning.
In summary, Option 4 captures the correct planning relationship: 14,000 minus 11,200 equals 2,800, which is the allocation for sampling risk in this MUS planning context. The other options either misinterpret the probabilistic implications of confidence level, misstate what UML implies, or make absolute conclusions about materiality that depend on sample results and professional judgment rather than a fixed parameter.

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