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 σ = 60. Let μ denote the true average compressive strength.
a. What are the appropriate null and alternative hypotheses?
b. Let X denote the sample average compressive strength for n = 10 randomly selected specimens. Consider the test procedure with test statistic  itself (not standardized). If  = 1340, should H0 be rejected using a significance level of .01?
c. What is the probability distribution of the test statistic when μ = 1350? For a test with α = .01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1350 (a type II error)?