Which error occurs when you fail to reject the null hypothesis when it is false?

Which error occurs when you fail to reject the null hypothesis when it is false?

• A. Type II error
• B. Type III error
• C. Type I error
• D. Precision error

Answer: (A)

In hypothesis testing, you compare what you observe to a null hypothesis and decide whether to reject it or not. The error that occurs when you fail to reject the null hypothesis even though it is actually false is a Type II error. It’s a false negative: you miss detecting a real effect or difference. The chance of this happening is called beta, and the test’s power is 1 minus beta, which tells you how likely you are to detect a true effect. Power increases with larger sample sizes, greater effect sizes, and a more lenient significance level, all of which make it easier to reveal that the null is false. The other terms don’t describe this situation: a Type I error is rejecting a true null (a false positive), and Type III and precision error aren’t standard terms for this context.

In hypothesis testing, you compare what you observe to a null hypothesis and decide whether to reject it or not. The error that occurs when you fail to reject the null hypothesis even though it is actually false is a Type II error. It’s a false negative: you miss detecting a real effect or difference. The chance of this happening is called beta, and the test’s power is 1 minus beta, which tells you how likely you are to detect a true effect.

Power increases with larger sample sizes, greater effect sizes, and a more lenient significance level, all of which make it easier to reveal that the null is false. The other terms don’t describe this situation: a Type I error is rejecting a true null (a false positive), and Type III and precision error aren’t standard terms for this context.