For the data of Exercise 5.16, sketch the power curve for rejecting H0: μ ≤ 38 by determining PWR(μa) for the following values of μ in the alternative hypothesis: 39, 40, 41, 42, 43, and 44.
a. Interpret the values on your curve.
b. Without actually recalculating the values for PWR(μ), sketch the power curve for α = .025 and n = 50.
c. Without actually recalculating the values for PWR(μ), sketch the power curve for α = .05 and n = 20.
Exercise 5.16
A researcher wanted to test the hypotheses H0: μ ≤ 38 against Ha: μ > 38 with α = .05. A random sample of 50 measurements from a population yielded and s = 5.6.
a. What conclusions can you make about the hypotheses based on the sample information?
b. Could you have made a Type II error in this situation? Explain.
c. Calculate the probability of a Type II error if the actual value of μ is at least 39.
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