This applet illustrates the power of statistical tests. The setting is the same as Chapter 15 of TPS 3e : testing hypotheses about the mean of a normal distribution whose standard deviation you know. Finding the power of a test assumes that you have set a fixed significance level α for the test. Review the STATISTICAL SIGNIFICANCE applet to recall how tests with significance level α work.
To set up the test, enter your information: What null hypothesis H0 about the mean μ do you want to test? Is your alternative hypothesis one-sided high, one-sided low, or two-sided? What level of significance α do you require? How many observations do you have (50 or fewer)? What is the known value of the standard deviation σ? Finally, against what specific alternative value of the mean μ do you want to find the power? When you have entered your information, click Update.
The top curve shows the sampling distribution of the sample mean when your null hypothesis is true. The yellow area under this curve is α, the probability of rejecting H0 when it is really true. The bottom curve shows the sampling distribution of when your chosen alternative is true. The red area under this curve is the power, the probability of rejecting H0 when the alternative is really true.