Which of the following is not a true statement about error in hypothesis testing?

• A. The probability of a Type I error is denoted by $\beta$.
• B. A Type I error occurs when the null hypothesis is rejected when it is actually true.
• C. A Type II error occurs when the null hypothesis is not rejected when it is actually false.
• D. Reducing the probability of a Type I error may increase the probability of a Type II error.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the definitions of Type I and Type II errors in hypothesis testing. A Type I error occurs when the null hypothesis (H0) is rejected even though it is true, and a Type II error occurs when the null hypothesis is not rejected even though it is false.
2. Step 2: Recall the notation used for the probabilities of these errors. The probability of a Type I error is denoted by \(\alpha\), and the probability of a Type II error is denoted by \(\beta\).
3. Step 3: Analyze each statement given in the problem: verify if the statement about the probability of Type I error being \(\beta\) is correct or not, based on the standard notation.
4. Step 4: Confirm that the statements about the definitions of Type I and Type II errors are true, as they align with the standard definitions.
5. Step 5: Understand the trade-off between Type I and Type II errors: reducing \(\alpha\) (Type I error probability) often increases \(\beta\) (Type II error probability), which is a well-known concept in hypothesis testing.