Question

fill in the blank.
a type i error is the mistake of ______ when it is actually true.

a. rejecting the alternative hypothesis
b. rejecting the null hypothesis
c. failing to reject the alternative hypothesis
d. failing to reject the null hypothesis

Explanation:

In hypothesis testing, a Type I error occurs when we wrongly reject the null hypothesis ($H_0$) while it is actually true. The null hypothesis is the default assumption. Rejecting it when it's true is the definition of a Type I error. Options A and C involve the alternative hypothesis ($H_1$), which is not relevant to the definition of Type I error. Option D is about failing to reject the null hypothesis (which would be a Type II error if the null were false, but not a Type I error).

Answer:

B. rejecting the null hypothesis