A type II error isa) failing to reject the null when it is false b) rejecting the null when it is true

Explanation of Type II Error

A Type II error occurs in statistical hypothesis testing when the following happens:

1. Null Hypothesis (H0) - This is the hypothesis that indicates no effect or no difference, essentially the status quo.
2. Alternative Hypothesis (H1) - This is what you want to prove or find evidence for, indicating that there is an effect or a difference.

Understanding Errors

• Type I Error: This error refers to rejecting the null hypothesis when it is actually true. This means you are concluding there is an effect when there is not.
• Type II Error: In contrast, a Type II error occurs when you fail to reject the null hypothesis when it is, in fact, false. This means you conclude there is no effect when there actually is one.

Conclusions

Given the options:

• a) Failing to reject the null when it is false (this defines a Type II error)
• b) Rejecting the null when it is true (this defines a Type I error)

Final Answer

Therefore, the correct answer is a) failing to reject the null when it is false.