Sample size calculations for hypothesis tests are based on the trade off between Type I and Type II errors. The Type I error, or α, is the probability of rejecting the null hypothesis when it is true. The Type II error, or β, is the probability of not rejecting the null hypothesis when it is false. Generally you would like α and β to be small. Power, or 1 - β, is the probability of rejecting the null hypothesis when it is false.
Figure 17.1 Power Animation for One Sample Mean
