AU-C 530 requires that when a population contains individually significant items, these should typically be tested 100% while sampling can be applied to the remaining population, ensuring all items have a chance of selection. The key facts are that 35 invoices are individually significant (48% of the balance) and the auditor needs to test occurrence of the remaining purchases. Answer A correctly prescribes testing all individually significant items and then applying appropriate sampling to the remainder. Answer B violates the principle of testing significant items, Answer C inappropriately biases selection toward small items, and Answer D incorrectly suggests inquiry alone is sufficient for a substantive assertion. The professional judgment framework is: stratify the population by separating individually significant items for 100% examination, then apply sampling techniques to the remaining population to achieve appropriate audit coverage.

AU-C 530 recognizes monetary-unit sampling (MUS) as particularly effective for substantive testing when the auditor wants higher selection probability for larger recorded amounts while maintaining coverage of the entire population. The key facts are that PP&E additions vary significantly in size, the auditor wants to reduce risk of missing large misstatements, and full population coverage is desired. Answer A correctly identifies MUS as the optimal method because it automatically gives larger items higher selection probability while still allowing any item to be selected. Answer B violates random selection principles and may not be representative, Answer C inappropriately biases selection toward small items contrary to the stated objective, and Answer D violates the fundamental principle that sampling requires selection from the defined population. The professional judgment framework is: when testing populations with high variability and concern about large misstatements, MUS provides optimal coverage by probability-weighting selection by recorded amount.

AU-C 530 requires that when an auditor needs to quantify sampling risk and project results to the population, statistical sampling methods must be used. The key facts are that the engagement partner specifically wants quantification of sampling risk and the ability to project results, which are hallmarks of statistical sampling. Statistical attribute sampling (Answer B) is the correct choice because it provides a mathematical basis for measuring sampling risk and allows the auditor to make quantitative statements about the population based on sample results. Non-statistical attribute sampling (Answer A) cannot provide quantified sampling risk conclusions, monetary-unit sampling (Answer C) is designed for substantive testing of monetary amounts rather than control deviations, and judgmental selection (Answer D) violates the fundamental sampling principle that all items must have a chance of selection. The professional judgment framework is: when quantification of sampling risk is required for controls testing, use statistical attribute sampling with proper random selection methods.

AU-C 530 requires separate evaluation of control deviations and monetary misstatements, with consideration of whether findings indicate systemic issues requiring expanded procedures. The key facts are that one control deviation (missing approval) and one monetary misstatement ($1,200 over-refund) were identified in different transactions. Answer A correctly requires treating these as separate issues - the control deviation for evaluating control effectiveness and the misstatement for projecting to the population and comparing to tolerable misstatement. Answer B inappropriately attempts to offset current year findings with prior year results, Answer C fails to project the identified misstatement to the population, and Answer D incorrectly dismisses the relevance of authorization controls to financial reporting. The professional judgment framework is: evaluate control deviations and monetary misstatements separately, project each type of finding appropriately, and consider whether the nature of errors indicates broader issues requiring additional audit procedures.

AU-C 530 specifies that sample size for substantive tests of details depends on tolerable misstatement, expected misstatement, and the assessed risk of material misstatement for the relevant assertion. The key facts are that this is substantive testing of accounts receivable existence through confirmations, with a population containing both large and small balances. Answer B correctly identifies the three primary factors required by auditing standards for substantive sampling. Answer A references operational metrics rather than audit risk factors, Answer C incorrectly suggests electronic invoicing eliminates confirmation requirements, and Answer D inappropriately links payroll controls to receivables confirmation sample size. The professional judgment framework for substantive sampling is: determine (1) the maximum misstatement you can accept, (2) the misstatement you expect to find, and (3) the risk assessment for the assertion being tested, then use these to calculate appropriate sample size.

AU-C 530 requires that control test results be evaluated by comparing the sample deviation rate to the tolerable deviation rate while considering sampling risk, particularly when the control addresses fraud risks. The key facts are that 2 deviations were found in 50 items (4% deviation rate), the control is important for fraud prevention, and tolerable deviation rate was set low. Answer B correctly requires evaluation against tolerable rate with consideration of sampling risk and potential need for revised audit approach. Answer A fails to properly evaluate results against tolerable rate, Answer C incorrectly attempts to convert control deviations to dollar misstatements, and Answer D incorrectly claims controls testing is irrelevant to fraud risks. The professional judgment framework for evaluating control deviations is: calculate the sample deviation rate, consider sampling risk (especially for low tolerable rates), and determine whether planned reliance remains appropriate or whether the audit approach needs modification.

AU-C 530 requires that even when using non-statistical sampling, the auditor must project sample misstatements to the population and consider sampling risk when evaluating results against tolerable misstatement. The key facts are that non-statistical sampling was used, misstatements were identified (3 out of 60 items), and evaluation is needed. Answer B correctly requires projection of the sample misstatement rate to the population and consideration of sampling risk, which can be done judgmentally in non-statistical sampling. Answer A incorrectly suggests non-statistical samples cannot be evaluated, Answer C fails to project misstatements to the untested population, and Answer D inappropriately suggests manipulating audit thresholds to avoid addressing identified issues. The professional judgment framework is: non-statistical sampling still requires projection of sample results and consideration of sampling risk, though these are based on professional judgment rather than statistical calculation.

AU-C 530 establishes that sample size for tests of controls depends on three primary factors: tolerable deviation rate, expected deviation rate, and the desired level of assurance (allowable sampling risk). The key facts are that this is a test of controls over a three-way match, the auditor expects a low deviation rate, and the control is important for reducing substantive testing. Answer A correctly identifies all three factors required by professional standards for determining control test sample size. Answer B incorrectly references factors relevant to substantive testing rather than controls testing, Answer C confuses attribute sampling with variables sampling by focusing on monetary amounts, and Answer D incorrectly suggests related-party transactions require 100% testing for controls. The professional judgment framework is: for control testing sample size, always consider (1) how many deviations you can tolerate, (2) how many you expect to find, and (3) how confident you need to be in your conclusion.

AU-C 530 requires evaluating if sample deviation rate plus sampling risk exceeds tolerable in attribute sampling to assess reliance. The 1 deviation in 50 wires against 2% tolerable and 0% expected necessitates risk consideration for control effectiveness. This follows standards for projection and evaluation. Concluding effective or ignoring deviates from principles, and projecting dollars misapplies attribute method. Auditors consider risk in deviation assessments. A rule is to forgo reliance if upper deviation limit exceeds tolerable.

AU-C 530 identifies frequency, expected and tolerable deviation rates, and risk of assessing control risk too low as key for sample size in tests of controls. The weekly cash disbursement control requires reliance, so these factors determine sample size to ensure adequate evidence. This aligns with guidance for attribute sampling in recurring controls. Basing on weeks alone, materiality, or inherent risk only overlooks deviation and risk considerations. Auditors should scale samples to control frequency and risk for effective testing. A decision rule is to increase samples for frequent controls with higher planned reliance.