# Question

Again consider the Consolidated Power waste water situation. Remember that the power plant will be shut down and corrective action will be taken on the cooling system if the null hypothesis H0: μ ≤ 60 is rejected in favor of Ha: μ > 60. In this exercise we calculate probabilities of various Type II errors in the context of this situation.

a. Recall that Consolidated Power’s hypothesis test is based on a sample of n = 100 temperature readings and assume that s equals 2. If the power company sets α = .025, calculate the probability of a Type II error for each of the following alternative values of μ: 60.1, 60.2, 60.3, 60.4, 60.5, 60.6, 60.7, 60.8, 60.9, 61.

b. If we want the probability of making a Type II error when m equals 60.5 to be very small, is Consolidated Power’s hypothesis test adequate? Explain why or why not. If not, and if we wish to maintain the value of α at .025, what must be done?

c. The power curve for a statistical test is a plot of the power = 1 – β on the vertical axis versus values of μ that make the null hypothesis false on the horizontal axis. Plot the power curve for Consolidated Power’s test of H0: μ = 60 versus Ha: μ = 60 by plotting power = 1 – β for each of the alternative values of m in part a. What happens to the power of the test as the alternative value of m moves away from 60?

a. Recall that Consolidated Power’s hypothesis test is based on a sample of n = 100 temperature readings and assume that s equals 2. If the power company sets α = .025, calculate the probability of a Type II error for each of the following alternative values of μ: 60.1, 60.2, 60.3, 60.4, 60.5, 60.6, 60.7, 60.8, 60.9, 61.

b. If we want the probability of making a Type II error when m equals 60.5 to be very small, is Consolidated Power’s hypothesis test adequate? Explain why or why not. If not, and if we wish to maintain the value of α at .025, what must be done?

c. The power curve for a statistical test is a plot of the power = 1 – β on the vertical axis versus values of μ that make the null hypothesis false on the horizontal axis. Plot the power curve for Consolidated Power’s test of H0: μ = 60 versus Ha: μ = 60 by plotting power = 1 – β for each of the alternative values of m in part a. What happens to the power of the test as the alternative value of m moves away from 60?

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