Question

which of the following is not a true statement about error in hypothesis testing?
choose the correct answer below.
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 false.
c. a type i error is making the mistake of rejecting the null hypothesis when it is actually true.
d. the symbol \\( \alpha \\) represents the probability of a type i error.

Explanation:

• Type I error: It occurs when we reject the null hypothesis ($H_0$) when it is actually true. The probability of a Type I error is denoted by $\alpha$.
• Type II error: It occurs when we fail to reject the null hypothesis ($H_0$) when it is actually false.

Now let's check each option:

• Option A: A Type II error is indeed failing to reject $H_0$ when it is false. This is a correct statement.
• Option B: A Type I error is rejecting $H_0$ when it is true, not when it is false. This is an incorrect statement.
• Option C: A Type I error is rejecting $H_0$ when it is true. This is a correct statement.
• Option D: The symbol $\alpha$ represents the probability of a Type I error. This is a correct statement.

Answer:

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