The question asks: "Which of the following is NOT a true statement about error in hypothesis testing?"

Here are the choices:

A. A type II error is making the mistake of failing to reject the null hypothesis when it is actually false.
B. A type I error is making the mistake of rejecting the null hypothesis when it is actually true.
C. The symbol $\alpha$ represents the probability of a type I error.
D. A type I error is making the mistake of rejecting the null hypothesis when it is actually false.

Analysis:

1. Option A: True. A type II error involves failing to reject a false null hypothesis.
2. Option B: True. A type I error involves rejecting a true null hypothesis.
3. Option C: True. The probability of a type I error is denoted by $\alpha$, often called the "significance level."
4. Option D: NOT true. This misrepresents the definition of a type I error. Rejecting the null hypothesis when it is false is a correct decision, not an error.

Answer:

D. A type I error is making the mistake of rejecting the null hypothesis when it is actually false.

Would you like further clarification or additional examples?

5 Expanding Questions:

1. What is the definition of a type II error in hypothesis testing?
2. How can we minimize the probability of a type I error in practice?
3. What is the role of the significance level ($\alpha$) in hypothesis testing?
4. How are type I and type II errors related to statistical power?
5. What are real-life examples of type I and type II errors in research?

Tip: To reduce type I errors, adjust the significance level $\alpha$; however, this often increases the probability of type II errors, creating a tradeoff.