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 α 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 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 making the mistake of failing to reject the null hypothesis when it is actually false. This is a correct statement.
• Option B: A type I error is making the mistake of rejecting the null hypothesis when it is actually false. This is incorrect. A type I error is rejecting the null hypothesis when it is actually true.
• Option C: A type I error is making the mistake of rejecting the null hypothesis when it is actually 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.