e-Statistics

## Power of Test

What is the probability that we incorrectly reject the null hypothesis  when it is actually true? The probability of such an error is called the probability of type I error, and is exactly the significance level . But how about the probability that we incorrectly accept the null hypothesis  when it is actually false? Such probability is called the probability of type II error.

Given the current estimate of population mean and of standard deviation, it is possible to find

The value  is known as the power of the test, indicating how correctly can be accepted when it is actually true in the following hypothesis test problem

The power of the test can be calculated with a specific choice of the sample size

The power of the test increases as the sample size increases. Therefore, we can achieve the desired power  of the test instead by increasing a sample size . Furthermore, having prescribed the power  and the sample size , it is possible to derive the corresponding value .