Final answer:
The acceptable level of detection risk is inversely related to the extent of the substantive procedures. As the extent of these procedures increases, the acceptable level of detection risk decreases because auditors perform more tests, reducing the risk of missing material misstatements.
Step-by-step explanation:
The acceptable level of detection risk is inversely related to the extent of the substantive procedures. Detection risk refers to the risk that an auditor fails to detect a material misstatement in the financial statements. Therefore, as the extent of substantive procedures increases, auditors perform more tests and gather more evidence, which in turn lowers the acceptable level of detection risk because there is a higher likelihood of discovering material errors or fraud.
The correct answer to the student's question is c) extent of the substantive procedures. An inverse relationship means that as one factor increases, the other decreases. So, if auditors increase the extent of their substantive procedures (testing details of transactions and balances), they can accept a lower level of detection risk since their procedures are more likely to identify material misstatements.