By definition, a Type I error is ____.
a. rejecting a false H1
b. rejecting a false H0
c. rejecting a true H0
d. rejecting a true H1
To determine the correct answer, we need to understand the concepts of Type I error and hypothesis testing.
In hypothesis testing, we set up two competing hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis represents the status quo or no effect, while the alternative hypothesis suggests that there is an effect or a difference.
A Type I error occurs when we reject the null hypothesis (H0) when it is actually true. In simpler terms, it means that we mistakenly conclude that there is an effect or a difference when there isn't one in reality.
Now, let's analyze the options:
a. Rejecting a false H1: This means rejecting the alternative hypothesis when it is false, which doesn't align with the definition of Type I error.
b. Rejecting a false H0: This means rejecting the null hypothesis when it is false, which also doesn't align with the definition of Type I error.
c. Rejecting a true H0: This means rejecting the null hypothesis when it is true, which accurately represents the definition of Type I error.
d. Rejecting a true H1: This means rejecting the alternative hypothesis when it is true, which is not what Type I error refers to.
Therefore, the correct answer is c. Rejecting a true H0.