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2. A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with a = 60. Let u denote the true average compressive strength. a. What are the appropriate null and alternative hypotheses? b. If x = 1340 for a sample of 10, should null hypothesis be rejected using a significance level of .01? c. For a test with a = .01, what is the probability that the mixture will be judged unsatisfactory when in fact u = 1350 ? Hint: find ß the type II error for µ' = 1350. d. What sample size should you take to make sure that the type II error ß = .02 when u' = 1350 and a = .01, μo = 1300.