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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/m". The mixture will not be used unless experimental evidence indicates condusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with 65. Let denote the trve average compressive strength. (4) What are the appropriate null and aternative hypotheses? OH 1300 H 1.300 OH 1300 R1300 H 1,300 " 1,300 "1300 O 1300 (D) Let denote the sample averege compressive strength for n 11 randomly selected specimens. Consider the test procedure with test stttic ser (not standardced, Whuc is the probabilty distribution of the test statistic when H. is true O The test statistk has a normal distribution, O The test statisti has a tinomial dstritution O The test statistic has a gamma distribution. O The test statistk has an exponential dstriution. 1310, Srd the Pyale, (Round your answer to four decimal places.) Dvalue- 0 Should M be rejected usinga significance level of 0.017 O reject Mg do not reject , () What is the probabiity distribution of the test statistic when a,350 and n 117 O The test statistic has a gamma distribution. O The test statistic has an exponential distribution. The test statistic has a normal distritution. O The test statistic has a binomial distribution. State the mean and standard deviation (in KNm) of the test statistic. (Round your standard deviation to three decimal places.) mean standard deviation for a test with a 0.01, what is the probability that the mixture will be judged unsatistactory when in fact 1,350 (a type error) (Round your answer to fuur decimal places.)

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/m". The mixture will not be used unless experimental evidence indicates condusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with 65. Let denote the trve average compressive strength. (4) What are the appropriate null and aternative hypotheses? OH 1300 H 1.300 OH 1300 R1300 H 1,300 " 1,300 "1300 O 1300 (D) Let denote the sample averege compressive strength for n 11 randomly selected specimens. Consider the test procedure with test stttic ser (not standardced, Whuc is the probabilty distribution of the test statistic when H. is true O The test statistk has a normal distribution, O The test statisti has a tinomial dstritution O The test statistic has a gamma distribution. O The test statistk has an exponential dstriution. 1310, Srd the Pyale, (Round your answer to four decimal places.) Dvalue- 0 Should M be rejected usinga significance level of 0.017 O reject Mg do not reject , () What is the probabiity distribution of the test statistic when a,350 and n 117 O The test statistic has a gamma distribution. O The test statistic has an exponential distribution. The test statistic has a normal distritution. O The test statistic has a binomial distribution. State the mean and standard deviation (in KNm) of the test statistic. (Round your standard deviation to three decimal places.) mean standard deviation for a test with a 0.01, what is the probability that the mixture will be judged unsatistactory when in fact 1,350 (a type error) (Round your answer to fuur decimal places.)

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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**Title: Statistical Analysis of Compressive Strength in Construction Materials** **Introduction:** This exercise involves the statistical analysis of compressive strength for a mixture of pulverized fuel ash and Portland cement used in grouting. The objective is to determine if the mixture meets the specified compressive strength requirement of more than 1,300 kN/m². **Problem Statement:** Suppose the compressive strength for specimens of this mixture is normally distributed with a standard deviation, σ = 65. Let μ denote the true average compressive strength. --- **Part (a): Hypotheses Formulation** **Objective:** Determine the appropriate null and alternative hypotheses. - Null Hypothesis (\(H_0\)): μ = 1,300 - Alternative Hypothesis (\(H_a\)): μ > 1,300 Selecting correct hypotheses from options: - \(H_0: \mu = 1,300\) - \(H_a: \mu > 1,300\) --- **Part (b): Statistical Distribution for Test Statistic** **Objective:** Identify the probability distribution of the test statistic \( \overline{X} \) with sample size n = 11. - Given the test procedure is based on the sample average compressive strength \( \overline{X} \). Test statistic possible distributions: - The test statistic has a normal distribution. With \( \overline{x} = 1,350 \), calculate \( P\)-value: \( P\)-value = 0.0009 - Decision: Should \( H_0 \) be rejected using a significance level of 0.01? Options: - Reject \( H_0 \). --- **Part (c): Probability Distribution of Test Statistic** **Objective:** Determine the distribution of the test statistic when n = 11 and \( \overline{x} = 1,350 \). Options: - The test statistic has a normal distribution (correct answer). State mean and standard deviation (in kN/m²) of the test statistic: - Mean: 1,300 - Standard Deviation: 19.5910 **Probability of Type II Error for α = 0.01:** - Probability (round to four decimal places): 0.3129 **Conclusion:** For α = 0.01, the probability of a Type II error, where the mixture is incorrectly judged as unsatisfactory when μ = 1,
Transcribed Image Text:**Title: Statistical Analysis of Compressive Strength in Construction Materials** **Introduction:** This exercise involves the statistical analysis of compressive strength for a mixture of pulverized fuel ash and Portland cement used in grouting. The objective is to determine if the mixture meets the specified compressive strength requirement of more than 1,300 kN/m². **Problem Statement:** Suppose the compressive strength for specimens of this mixture is normally distributed with a standard deviation, σ = 65. Let μ denote the true average compressive strength. --- **Part (a): Hypotheses Formulation** **Objective:** Determine the appropriate null and alternative hypotheses. - Null Hypothesis (\(H_0\)): μ = 1,300 - Alternative Hypothesis (\(H_a\)): μ > 1,300 Selecting correct hypotheses from options: - \(H_0: \mu = 1,300\) - \(H_a: \mu > 1,300\) --- **Part (b): Statistical Distribution for Test Statistic** **Objective:** Identify the probability distribution of the test statistic \( \overline{X} \) with sample size n = 11. - Given the test procedure is based on the sample average compressive strength \( \overline{X} \). Test statistic possible distributions: - The test statistic has a normal distribution. With \( \overline{x} = 1,350 \), calculate \( P\)-value: \( P\)-value = 0.0009 - Decision: Should \( H_0 \) be rejected using a significance level of 0.01? Options: - Reject \( H_0 \). --- **Part (c): Probability Distribution of Test Statistic** **Objective:** Determine the distribution of the test statistic when n = 11 and \( \overline{x} = 1,350 \). Options: - The test statistic has a normal distribution (correct answer). State mean and standard deviation (in kN/m²) of the test statistic: - Mean: 1,300 - Standard Deviation: 19.5910 **Probability of Type II Error for α = 0.01:** - Probability (round to four decimal places): 0.3129 **Conclusion:** For α = 0.01, the probability of a Type II error, where the mixture is incorrectly judged as unsatisfactory when μ = 1,
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