In the context of hypothesis testing, when is a researcher at risk of making a ${\mathrm{Type}}^{\mathrm{II}}$ error?

• A. When the $\mathrm{null} \mathrm{hypothesis}$ is false but the researcher fails to reject it
• B. When the $\mathrm{null} \mathrm{hypothesis}$ is true and the researcher fails to reject it
• C. When the $\mathrm{alternative} \mathrm{hypothesis}$ is true and the researcher rejects the $\mathrm{null} \mathrm{hypothesis}$
• D. When the $\mathrm{null} \mathrm{hypothesis}$ is true and the researcher rejects it

Answer: (A)

Verified step by step guidance

1. Understand the definitions of Type I and Type II errors in hypothesis testing: A Type I error occurs when the null hypothesis is true but is incorrectly rejected, while a Type II error occurs when the null hypothesis is false but is not rejected.
2. Identify the condition for a Type II error: It happens when the null hypothesis is actually false (meaning the alternative hypothesis is true), but the researcher fails to reject the null hypothesis based on the sample data.
3. Analyze each option given in the problem by comparing it to the definition of a Type II error: Check whether the null hypothesis is false and whether the researcher fails to reject it.
4. Recognize that the correct scenario for a Type II error is exactly when the null hypothesis is false but the researcher does not reject it, which means missing a true effect or difference.
5. Conclude that the correct answer corresponds to the situation where the null hypothesis is false but the researcher fails to reject it, as this matches the definition of a Type II error.