Question

a type i error occurs in hypothesis testing when we ________

a. fail to reject the alternative hypothesis and the alternative hypothesis is false
b. fail to reject the null hypothesis and the null hypothesis is false
c. reject the alternative hypothesis and the alternative hypothesis is true
d. reject the null hypothesis and the null hypothesis is true

Explanation:

A Type I error occurs when we reject the null hypothesis ($H_0$) when it is actually true. Let's analyze each option:

• Option A: Failing to reject the alternative hypothesis ($H_1$) when it is false is not a Type I error.
• Option B: Failing to reject the null hypothesis when it is false is a Type II error.
• Option C: Rejecting the alternative hypothesis when it is true is not a Type I error.
• Option D: Rejecting the null hypothesis when it is true is the definition of a Type I error.

Answer:

D. reject the null hypothesis and the null hypothesis is true