A mixture of pulverized fuel ash and Portland cement to be used for grouting sho

Question

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 = 70. Let denote the true average compressive strength.

If X = 1340, find the P-value. (Round your answer to four decimal places.)

State the mean and standard deviation of the test statistic.

For a test with = 0.01, 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.)

Explanation / Answer

Mean = 1300

Standard deviation = 70

The test statistic Z = (X - mean)/SD

= (1340 - 1300)/70

= 0.57

P-value = P(Z > 0.57)

= 1 - P(Z < 0.57)

= 1 - 0.7157 = 0.2843

P(X > 1340) = P((x - mean )/SD > (1340 - 1350)/70)

= P(Z > -0.14)

= 1 - P(Z < -0.14)

= 1 - 0.4443

= 0.5557

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