If we plot the probability of accepting H 0 : = 0 versus various values of and connect the points with a smooth

If we plot the probability of accepting H₀: μ = μ0 versus various values of μ and connect the points with a smooth curve, we obtain the operating characteristic curve (or the OC curve) of the test procedure. These curves are used extensively in industrial applications of hypothesis testing to display the sensitivity and relative performance of the test. When the true mean is really equal to μ₀, the probability of accepting H₀ is 1 – α. 

(a) Construct an OC curve for Exercise 9-15, using values of the true mean μ of 178, 181, 184, 187, 190, 193, 196, and 199.

(b) Convert the OC curve into a plot of the power function of the test.