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 = 66. Let μ denote the true average compressive strength.

(b) Let X denote the sample average compressive strength for n = 14 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when H₀ is true? If X = 1340, find the P-value. (Round your answer to four decimal places.) P-value =

(c) What is the probability distribution of the test statistic when μ = 1350?

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

mean		KN/m2
standard deviation		KN/m2

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.)

i have bolded the FOUR questions that need to be answered! please answer all four...

Answer 1

(b)

Since population is normally distributed so test statistics will also have normal distribution.

(c)

The sampling distribution of sample mean will be approximately normal distribution with mean

and standard deviation is

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Test is right tailed so critical value of z for α = 0.01 is 2.33. The critical value of sample mean for which we will reject the null hypothesis is

Now test statistics z such that and μ = 1350 will be

So type II error is

P(z < -0.50) = 0.3085