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 σ = 56. Let μ denote the true average compressive strength

Let Xdenote the sample average compressive strength for n = 10 randomly selected specimens. Consider the test procedure with test statistic

Xitself (not standardized).

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

(b).State the mean and standard deviation of the test statistic. (Round your standard deviation to three decimal places.)

(c)For a test with α = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1350 (a type II error)? (Round your answer to four decimal places.)

Answer 1

(a)

The p-value is: 0.0119

(b)

The probability distribution of sample mean will be normal distribution with mean

and standard deviation

(C)

Hence, type II error is 0.3085.