Which statement below is consistent with making a ${\mathrm{Type}}^{\mathrm{I}}$ error in hypothesis testing?

• A. Failing to reject the $H_0$ when it is actually true
• B. Failing to reject the $H_0$ when it is actually false
• C. Rejecting the $H_0$ when it is actually true
• D. Rejecting the $H_0$ when it is actually false

Answer: (C)

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 we reject the null hypothesis even though it is actually true, and a Type II error occurs when we fail to reject the null hypothesis even though it is actually false.
2. Identify the null hypothesis (H0) and the alternative hypothesis (H1) in the context of the problem, as these form the basis for making decisions and errors.
3. Analyze each statement given in the problem and classify it according to the error types: For example, 'Failing to reject the null hypothesis when it is actually true' means correctly accepting H0, so no error.
4. Recognize that 'Rejecting the null hypothesis when it is actually true' matches the definition of a Type I error, because the null hypothesis is true but is incorrectly rejected.
5. Conclude that the statement consistent with making a Type I error is 'Rejecting the null hypothesis when it is actually true' based on the definitions and analysis.