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Hello, I am having trouble with section (c) and the last question for this problem

Hello, I am having trouble with section (c) and the last question for this problem

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Hello, I am having trouble with section (c) and the last question for this problem 

A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 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 o = 65. Let μ denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? O Ho: μ> 1,300 H₂: μ = 1,300 |Ο Hg: μ < 1,300 H₂: μ = 1,300 OH = 1,300 H₂:μ 1,300 Ho: μ = 1,300 Ha: μ< 1,300 Ho: μ = 1,300 Ha: μ> 1,300 (b) Let X denote the sample average compressive strength for n = 13 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when Ho is true? O The test statistic has a gamma distribution. O The test statistic has an exponential distribution. O The test statistic has a normal distribution. O The test statistic has a binomial distribution. If X = 1,340, find the P-value. (Round your answer to four decimal places.) P-value = 0.0132 Should Ho be rejected using a significance level of 0.01? O reject Ho O do not reject Ho (c) What is the probability distribution of the test statistic when μ = 1,350 and n = 13? O The test statistic has a normal distribution. O The test statistic has a binomial distribution. O The test statistic has a gamma distribution. O The test statistic has an exponential distribution. State the mean and standard deviation (in KN/m2) of the test statistic. (Round your standard deviation to three decimal places.) KN/m² mean 1350 2.7737 standard deviation X KN/m² For a test with a = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1,350 (a type II error)? (Round your answer to four decimal places.) 0.9973 X You may need to use the appropriate table in the Appendix of Tables to answer this question.
Transcribed Image Text:A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1,300 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 o = 65. Let μ denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? O Ho: μ> 1,300 H₂: μ = 1,300 |Ο Hg: μ < 1,300 H₂: μ = 1,300 OH = 1,300 H₂:μ 1,300 Ho: μ = 1,300 Ha: μ< 1,300 Ho: μ = 1,300 Ha: μ> 1,300 (b) Let X denote the sample average compressive strength for n = 13 randomly selected specimens. Consider the test procedure with test statistic X itself (not standardized). What is the probability distribution of the test statistic when Ho is true? O The test statistic has a gamma distribution. O The test statistic has an exponential distribution. O The test statistic has a normal distribution. O The test statistic has a binomial distribution. If X = 1,340, find the P-value. (Round your answer to four decimal places.) P-value = 0.0132 Should Ho be rejected using a significance level of 0.01? O reject Ho O do not reject Ho (c) What is the probability distribution of the test statistic when μ = 1,350 and n = 13? O The test statistic has a normal distribution. O The test statistic has a binomial distribution. O The test statistic has a gamma distribution. O The test statistic has an exponential distribution. State the mean and standard deviation (in KN/m2) of the test statistic. (Round your standard deviation to three decimal places.) KN/m² mean 1350 2.7737 standard deviation X KN/m² For a test with a = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1,350 (a type II error)? (Round your answer to four decimal places.) 0.9973 X You may need to use the appropriate table in the Appendix of Tables to answer this question.
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