Practice Power of a Test in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The probability that a hypothesis test correctly rejects a false null hypothesis. Power = P(\text{reject } H_0 \mid H_0 \text{ is false}) = 1 - \beta, where \beta is the probability of a Type II error.
Power is your test's ability to detect a real effect when one exists. A test with high power is like a sensitive metal detector—it won't miss a coin buried in the sand. A test with low power is like searching with your eyes—you'll miss things that are actually there. You want power to be high (typically 0.80 or above).
Example 1
mediumA test has \alpha=0.05 and \beta=0.20. Calculate the power and interpret it. If the researcher wants Power=0.90, what must \beta become?
Example 2
hardFor testing H_0: \mu=100 vs H_a: \mu=105, with \sigma=10, n=25, \alpha=0.05: calculate the rejection region and power of the test.
Example 3
easyList four factors that increase the power of a hypothesis test, and explain the direction of each effect.
Example 4
hardA study fails to reject H_0 and concludes 'there is no effect.' Critique this conclusion using the concept of power, and explain what information is needed before accepting this conclusion.