The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with σ = .3 and that  = 5.25.
a. Does this indicate conclusively that the true average percentage differs from 5.5?
b. If the true average percentage is μ = 5.6 and a level α = .01 test based on n = 16 is used, what is the probability of detecting this departure from H0?
c. What value of n is required to satisfy α = .01 and β(5.6) = .01?