Final answer:
A Type II error in auditing refers to the risk of not detecting a material misstatement that actually exists. This kind of error is analogous to someone incorrectly believing that their rock climbing equipment is safe when it is not.
Step-by-step explanation:
The risk that an auditor's procedures will lead to a conclusion that a material misstatement in an account balance does not exist when, in fact, a misstatement does exist, is known as a Type II error.
This is similar to the risk faced by Frank who assumes his rock climbing equipment is safe when, in reality, it is not. A Type II error in auditing is the failure to detect a material misstatement that actually exists, which can be thought of as the risk of falsely believing the financial statements are free from material misstatement (the null hypothesis) when they are not.
Various methods, such as power analysis, can help estimate the likelihood of a Type II error, taking into account sample size, effect size, and the variance associated with the measure used.