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A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of mere than 1,300 K/m?. 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 withg 69. Let denote the true average compressive strength. (a) What are the appropriate nul and altermative hypetheses? H 1.300 H 1.300 M 1.300 1300 H -1.300 H> 1.300 H 1.300 H 1.300 H 1.300 H 1.300 (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 H, is true? • The test statistic has a normal distributien. O The test statistic has a binomial distribution. O The test statistie has an aunecantial distrtion

A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of mere than 1,300 K/m?. 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 withg 69. Let denote the true average compressive strength. (a) What are the appropriate nul and altermative hypetheses? H 1.300 H 1.300 M 1.300 1300 H -1.300 H> 1.300 H 1.300 H 1.300 H 1.300 H 1.300 (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 H, is true? • The test statistic has a normal distributien. O The test statistic has a binomial distribution. O The test statistie has an aunecantial distrtion

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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/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 vwith a = 69. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? O H: H = 1,300 H:u# 1,300 O H,: H = 1,300 H: u< 1,300 O H,: H= 1,300 H:H > 1,300 Ο Η , μ< 1,300 Hiu = 1,300 O H,: 4 > 1,300 H: H = 1,300 (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 H, is true? O The test statistic has a normal distribution. O The test statistic has a binomial distribution. O The test statistic has an exponential distribution. O The test statistic has a gamma distribution. If X = 1,340, find the P-value. (Round your answer to four decimal places.) P-value = Should H, be rejected using a significance level of 0.01? O reject H. O do not reject H. (c) What is the probability distribution of the test statistic when u = 1,350 and n = 15? O The test statistic has a binomial distribution. O The test statistic has a normal distribution. O The test statistic has an exponential distribution. O The test statistic has a gamma distribution. State the mean and standard deviation (in KN/m) of the test statistic. (Round your standard deviation to three decimal places.) mean KN/m? standard deviation KN/m? For a test with a = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact u = 1,350 (a type II error)? (Round your answer to four decimal places.)
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 vwith a = 69. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? O H: H = 1,300 H:u# 1,300 O H,: H = 1,300 H: u< 1,300 O H,: H= 1,300 H:H > 1,300 Ο Η , μ< 1,300 Hiu = 1,300 O H,: 4 > 1,300 H: H = 1,300 (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 H, is true? O The test statistic has a normal distribution. O The test statistic has a binomial distribution. O The test statistic has an exponential distribution. O The test statistic has a gamma distribution. If X = 1,340, find the P-value. (Round your answer to four decimal places.) P-value = Should H, be rejected using a significance level of 0.01? O reject H. O do not reject H. (c) What is the probability distribution of the test statistic when u = 1,350 and n = 15? O The test statistic has a binomial distribution. O The test statistic has a normal distribution. O The test statistic has an exponential distribution. O The test statistic has a gamma distribution. State the mean and standard deviation (in KN/m) of the test statistic. (Round your standard deviation to three decimal places.) mean KN/m? standard deviation KN/m? For a test with a = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact u = 1,350 (a type II error)? (Round your answer to four decimal places.)
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