Which of the following is an accurate definition of a Type ${\mathrm{II}}_{}$ error in hypothesis testing?

• A. Rejecting the null hypothesis ($H_0$) when it is actually true
• B. Failing to reject the null hypothesis ($H_0$) when it is actually false
• C. Accepting the alternative hypothesis ($H_1$) when the null hypothesis ($H_0$) is true
• D. Rejecting the alternative hypothesis ($H_1$) when it is actually false

Answer: (B)

Verified step by step guidance

1. Understand the context of hypothesis testing, where we have a null hypothesis (\(H_0\)) and an alternative hypothesis (\(H_a\)).
2. Recall that a Type I error occurs when we reject the null hypothesis (\(H_0\)) even though it is actually true.
3. Recognize that a Type II error happens when we fail to reject the null hypothesis (\(H_0\)) even though it is actually false.
4. Note that 'failing to reject \(H_0\) when it is false' means we miss detecting an effect or difference that actually exists.
5. Therefore, the accurate definition of a Type II error is: failing to reject the null hypothesis when it is actually false.