A mixture of fuel ash and cement is to be used for grouting and should have a compressive strength of more than 1300 KN/m2 . The mixture cannot be used unless the experimental evidence indicates conclusively that the strength specification has been met. State the relevant hypotheses and describe the type I and type II errors in the context of this problem.

Explanation:

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 ? = 68. Let ? denote the true average compressive strength.

(b) Let

X

denote the sample average compressive strength for n = 11 randomly selected specimens. Consider the test procedure with test statistic X and rejection region x ? 1331.26. What is the probability distribution of the test statistic when H0 is true? (Round your standard deviation to three decimal places.)

(c) What is the probability distribution of the test statistic when

? = 1350? (Round your standard deviation to three decimal places.)

Using the test procedure of part (b), what is the probability that the mixture will be judged unsatisfactory when in fact

? = 1350 (a type II error)? (Round your answer to four decimal places.)

(d) How would you change the test procedure of part (b) to obtain a test with significance level 0.05? (Round your answer to two decimal places.) Replace 1331.26 KN/m2 wit

What impact would this change have on the error probability of part (c)? (Round your answer to four decimal places.)

The probability that the mixture will be judged unsatisfactory when in fact ? = 1350 will change to .

(e) Consider the standardized test statistic

Z = (X ? 1300)/(?/n).

What are the values of Z corresponding to the rejection region of part (b)? (Round your answer to two decimal places.)

answer:

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