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. (a) What are the appropriate null and alternative hypotheses? H0: = 1300 Ha: < 1300 H0: = 1300 Ha: 1300 H0: < 1300 Ha: = 1300 H0: > 1300 Ha: = 1300 H0: = 1300 Ha: > 1300 Correct: Your answer is correct. (b) Let X denote the sample average compressive strength for n = 15 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 binomial distribution. The test statistic has a gamma distribution. The test statistic has an exponential distribution. The test statistic has a normal distribution. Correct: Your answer is correct. 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 Correct: Your answer is correct. (c) What is the probability distribution of the test statistic when = 1350? The test statistic has a normal distribution. The test statistic has an exponential distribution. The test statistic has a gamma distribution. The test statistic has a binomial distribution. Correct: Your answer is correct. 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 = 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.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Explanation / Answer

a) The alternative hypothesis states that th emixture shoul dhave compressive strength more than 1300 KN/m^2. H0:mu=1300 H1;mu>1300

b) The test statistic has normal distribution.

c) For 1-sample t test,

t=(Xbar-mu)/SE(xbar)=(1340-1300)/(70/sqrt 15)=2.21

p value is 0.0221.

p valu ei snot less than alpha=0.01. Do not reject H0.

c) Test statistic has normal distribution.

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