Statistics: hypotheses tests. Can you make this easier for me to understand?

Question

If α = 0.3, and β = .40, complete the following questions by inserting the appropriate probability of each.

The statistical decision is to reject the null, and H0 is really true (i.e., a type I error).

The statistical decision is to fail to reject null, and H0 is really true (i.e., correct decision).

The statistical decision is to the reject the null, and H0 is really false (i.e., power).

The statistical decision is to fail to reject the null, and H0 is really false (i.e., a Type II error).

Could you just get me started on solving these? I'm not sure how to apply α or β.

Answer 1

Okay, go read the definitions of Type 1 and Type 2 errors again. The definition of α = Type 1 error. β = Type 2 error. To understand what they mean, draw out a distribution graph (I'm sure it's in your book) with α and β and think about what each portion means. *I have a feeling that α = 0.03 and not 0.3 because that is a little high, but if not, then these are the answers:

The statistical decision is to reject the null, and H0 is really true (i.e., a type I error).

Answer: α = 0.3

The statistical decision is to fail to reject null, and H0 is really true (i.e., correct decision).

Answer: 1-α = 0.7

*this is the probability that the test WON'T make a Type l error.

The statistical decision is to the reject the null, and H0 is really false (i.e., power).

Answer: 1-β = 0.6

*this is the probability that the test WON'T make a Type ll error.

The statistical decision is to fail to reject the null, and H0 is really false (i.e., a Type II error).

Answer: β = 0.4