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 particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.30 and that x = 5.25.
(a) Compute the test statistic value. Round your answer to two decimal places.
(b) If the true average percentage is ? = 5.6 and a level ? = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H0? (Round your answer to four decimal places.)
(c) What value of n is required to satisfy ? = 0.01 and ?(5.6) = 0.01? (Round your answer up to the next whole number.)