Final answer:
Detection risk in auditing is inversely related to the level of assurance from audit evidence, similar to how a lower level of significance (α) in hypothesis testing requires more substantial evidence to avoid Type I errors. To lower detection risk, auditors might increase sample sizes or perform more thorough tests.
Step-by-step explanation:
The acceptable level of detection risk is indeed inversely related to the degree of assurance provided by the audit evidence from tests of controls. Detection risk pertains to the risk that auditors will not catch material misstatements in the financial statements. When auditors design their audit plans, they must consider various types of risks, including detection risk. The level of significance (or alpha, α) in hypothesis testing is an important concept, as it is the probability of committing a Type I error, which occurs when the null hypothesis is incorrectly rejected. The lower the α, the higher the level of assurance the auditors need, as they are accepting a lower chance of making such an error.
To reduce the detection risk, auditors might increase the extent or change the nature of their audit procedures, such as performing more detailed tests. This is conceptually similar to decreasing the alpha (α) in statistical hypothesis testing, where a smaller α requires more substantial evidence to conclude that a significant effect exists (conclusion e). Similarly, in planning an audit, if an auditor seeks a smaller error bound while maintaining the same level of confidence, they would need to increase their sample size (conclusion b) or adjust other elements of their audit methodology to enhance the reliability of the evidence collected.