A mixture of pulverized fuel ash and Portland cement to beused for grouting should have

Chapter 8, Problem 10

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A mixture of pulverized fuel ash and Portland cement to beused for grouting should have a compressive strength of morethan 1300 KN/m2. The mixture will not be used unless experimentalevidence indicates conclusively that the strengthspecification has been met. Suppose compressive strength forspecimens 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 strengthfor randomly selected specimens. Consider thetest procedure with test statistic and rejection region. What is the probability distribution of thetest statistic when H0 is true? What is the probability of atype I error for the test procedure?c. What is the probability distribution of the test statisticwhen ? Using the test procedure of part (b),what is the probability that the mixture will be judgedunsatisfactory when in fact (a type II error)?d. How would you change the test procedure of part (b) toobtain a test with significance level .05? What impactwould this change have on the error probability of part (c)?e. Consider the standardized test statistic. Whatare the values of Z corresponding to the rejection regionof part (b)?