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In: Statistics and Probability

A mixture of pulverized fuel ash and Portland cement to be used for grouting should have...

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 = 70. Let μ denote the true average compressive strength.

(a) What are the appropriate null and alternative hypotheses?

H0: μ = 1300
Ha: μ > 1300H0: μ > 1300
Ha: μ = 1300    H0: μ < 1300
Ha: μ = 1300H0: μ = 1300
Ha: μ ≠ 1300H0: μ = 1300
Ha: μ < 1300


(b) Let

X

denote the sample average compressive strength for n = 11 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?

The test statistic has a gamma distribution.The test statistic has an exponential distribution.    The test statistic has a normal distribution.The test statistic has a binomial distribution.


If

X = 1340,

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

Should H0 be rejected using a significance level of 0.01?

reject H0

do not reject H0    


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

The test statistic has an exponential distribution.The test statistic has a normal distribution.    The test statistic has a gamma distribution.The test statistic has a binomial distribution.


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.)

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Expert Solution

Answer: ---- Date: ----11/7/2019

orchestra answered 1 year ago
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