Which statement best describes the relationship among audit risk, materiality, and detection risk?

• A. Audit risk rises when materiality thresholds are lowered; detection risk is independent.
• B. Audit risk is the risk of a material misstatement not detected; materiality sets thresholds; detection risk is inversely related to the extent of evidence.
• C. Materiality determines detection risk directly, and audit risk is unrelated.
• D. Detection risk increases as both audit risk and materiality rise.

Answer: (B)

In auditing, the important idea is how risk, thresholds, and evidence work together. Audit risk is the chance that the auditor issues an incorrect opinion about the financial statements due to a material misstatement not being detected. Materiality sets the thresholds for what counts as a material misstatement—essentially guiding what the auditor considers important enough to matter. Detection risk is the risk that the audit procedures fail to detect a material misstatement; it is inversely related to the extent and quality of evidence gathered—the more thorough the evidence, the lower the detection risk.

The statement that best fits this interplay says: audit risk is the risk of a material misstatement not detected; materiality establishes thresholds; and detection risk moves inversely with the amount and quality of evidence. This captures the idea that you manage overall audit risk by adjusting how much and how well you test. If you lower materiality (tighter thresholds), you need more evidence to keep detection risk low and maintain the desired audit risk. If materiality is higher, you can accept more detection risk with less testing, still aiming for the target level of audit risk.

The other options misstate the relationships: detection risk is not independent and does depend on evidence; materiality does not directly determine detection risk without considering evidence; and detection risk does not simply rise with both audit risk and materiality in a straightforward way.