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

. Let m denote the true average compressive strength.

a. What are the appropriate null and alternative hypotheses?

b. Let denote the sample average compressive strength for randomly selected specimens. Consider the test procedure with test statistic and rejection region

. What is the probability distribution of the test statistic when H0 is true? What is the probability of a type I error for the test procedure?

c. What is the probability distribution of the test statistic when ? Using the test procedure of part (b), what is the probability that the mixture will be judged unsatisfactory when in fact (a type II error)?

d. How would you change the test procedure of part

(b) to obtain a test with significance level .05? What impact would this change have on the error probability of part (c)?

e. Consider the standardized test statistic

. What are the values of Z corresponding to the rejection region of part (b)?