I know that type I error definition is rejecting a null that is actually true.
In this problem the following definition of Type I error was given: “Type I error: incorrectly rejecting the null hypothesis when it should not be rejected.”
I’m confused on how these mean the same thing.
You’re right. Type 1 error is rejecting a null hypothesis that is actually true. If you don’t mind my asking, where did you get this definition? Schweser, perhaps?
Yes it was a Kaplan question so it was in their Q Bank. I thought of it like this: if type 1 error is rejecting a null that’s true then this could also be rephrased as incorrectly rejecting a null (same as the first part of rejecting a null in my original definition" when it should not be rejected (similar to that is actually true). That might not make sense how I put it but it briefly made sense.
I’ve seen quite a few poor quality problems from Kaplan-S when browsing this forum, so it doesn’t surprise me that it’s from them. The reasoning seems as you said. Still, that’s a horribly phrased definition and have the potential to cause confusion. The null hypothesis is known to be true for the type 1 error (this is not clear by Kaplan-S definition). As you know, the distinction between accepting a null hypothesis and not rejecting it is important when performing a hypothesis test. They are not the same.