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 std dev = 0.30 and that xbar = 5.25. H0 = mu = 5.5, Ha: mu not = 5.5. The rejection region(s) for an alpha
= 0.01 test is z <=-2.58 and z>=2.58. The test statistic value z = -3.33.
(a) if the true average percentage is mu = 5.6 and a level alpha = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H0?
(b) what value of n is required to satisfy alpha = 0.01 and Beta(5.6) = 0.01?