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 (sigma) = 0.3 and that x-bar = 5.25. a) Does this indicate conclusively that the true average percentage differs from 5.5? Conduct a hypothesis test at significance level a = 0.01.

b) If the true average percentage is (mu) = 5.6 and a level a = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H0? (i. e. what is the power of the test when ?? = 5.6? Recall, power = 1-P(type 2 error))