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Problem A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. Preliminary data analyses indicate that it is reasonable to apply a z-test. The hypotheses are
H0 = $1,200
H1 > 1,200
σ = $180
n = 38
α=0.10
Find the probability of a Type II error and the power for μ = $1075, $1100, $1150, $1175, $1190.
Use the values to sketch a power curve.