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

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

Answer: (B)

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 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 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 the statement 'Reducing the probability of a Type I error may increase the probability of a Type II error.' This is true because making the test more stringent to avoid false positives (Type I errors) can increase the chance of false negatives (Type II errors).
4. Step 4: Evaluate the statement 'The probability of a Type I error is denoted by \(\beta\).' This is incorrect because \(\beta\) represents the probability of a Type II error, not Type I.
5. Step 5: Confirm the remaining statements: 'A Type II error occurs when the null hypothesis is not rejected when it is actually false' and 'A Type I error occurs when the null hypothesis is rejected when it is actually true' are both true by definition.