Final answer:
The risk in question is known as a Type II error, which occurs when an auditor fails to detect a misstatement that actually exists. This error is a statistical concept important in auditing, linked to the incorrect acceptance of the null hypothesis, and influenced by factors like sample size, effect size, and variance.
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 type of error occurs when an auditor falsely accepts the null hypothesis (which suggests that no significant difference exists), even though the alternative hypothesis is the true state of affairs. In the context provided, a Type II error is akin to Frank going climbing, thinking his equipment is safe based on his flawed assessment, only to discover that his equipment was indeed not safe — the null hypothesis (his equipment is safe) was incorrectly accepted.
Type II error is an important concept in both auditing and statistics, as it highlights the probability of failing to detect a problem or a difference that actually exists. For auditors, minimizing this error is essential to ensure accuracy and reliability in their work. The likelihood of a Type II error can be influenced by various factors, including sample size, effect size (magnitude of the difference one is trying to detect), and the total variance associated with the measure used. Understanding and managing this type of error helps in making more informed decisions based on statistical evidence.