Statistics 10.6: Probability of the Power of the Test

What are the steps for finding the Power of the Test in a right-tailed test?

1. First we find β, probability of Type II error, by finding the critical value of the given level of significance.

Recall: What is a Type I error?

A Type I error is when you reject the null hypothesis when in reality it is true. The probability of making this error is denoted by alpha, α (aka the level of significance).

Recall: What is a Type II error?

A Type II error is when we fail/don't reject the null hypothesis when in reality it is false. (found not guilty when actually guilty) The probability of making this error is denoted by beta, β. This is known as an incorrect conclusion but a conclusion none the less.

What is the Power of the Test?

The Power of the Test is the probability of rejecting the null hypothesis H₀ when the alternative hypothesis H₁ is true, which is a correct conclusion. Denoted by 1-β and referred to as "P.O.T." the higher the P.O.T. the more likely test will reject the null when the alt is true.

What is Beta (β)?

Beta is the probability of making a Type II error. In other words, the probability of "accepting" H₀ when H₁ is true, which is an incorrect conclusion but a conclusion none the less.

Recall: Z-Score of p-hat

The z-score of p=hat is the sample proportion subtracted by the population proportion, divided by the standard deviation of the population.