Homework Help is Here – Start Your Trial Now!
Math
Probability
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 = 67. Let denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? Ho: μ< 1,300 H: 1,300 ⒸHO: H= 1,300 Ha: # 1,300 Ho: > 1,300 H:H= 1,300 ⒸHO: H= 1,300 H₂: > 1,300 Ho: μ= 1,300 H₂: < 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 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 binomial distribution. O The test statistic has a normal distribution. If X = 1,340, find the P-value. (Round your answer to four decimal places.) P-value= 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 = 1,350 and n = 15? O The test statistic has a gamma distribution. O The test statistic has a binomial distribution. O The test statistic has an exponential distribution. O The test statistic has a normal distribution. State the mean and standard deviation (in KN/m2) of the test statistic. (Round your standard deviation to three decimal places.) mean KN/m2 KN/m2 standard deviation 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.)

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 = 67. Let denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? Ho: μ< 1,300 H: 1,300 ⒸHO: H= 1,300 Ha: # 1,300 Ho: > 1,300 H:H= 1,300 ⒸHO: H= 1,300 H₂: > 1,300 Ho: μ= 1,300 H₂: < 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 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 binomial distribution. O The test statistic has a normal distribution. If X = 1,340, find the P-value. (Round your answer to four decimal places.) P-value= 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 = 1,350 and n = 15? O The test statistic has a gamma distribution. O The test statistic has a binomial distribution. O The test statistic has an exponential distribution. O The test statistic has a normal distribution. State the mean and standard deviation (in KN/m2) of the test statistic. (Round your standard deviation to three decimal places.) mean KN/m2 KN/m2 standard deviation 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.)

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
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question
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 = 67. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? Ho: μ< 1,300 H₂: μ = 1,300 O Ho: μ = 1,300 H₂: μ = 1,300 Ho: μ > 1,300 H₂: μ = 1,300 Ho: μ = 1,300 H a: μ> 1,300 ○ Ho: μ = 1,300 H₂: μ< 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 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 binomial distribution. The test statistic has a normal distribution. If X = 1,340, find the P-value. (Round your answer to four decimal places.) P-value = 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 = 15? O The test statistic has a gamma distribution. O The test statistic has a binomial distribution. The test statistic has an exponential distribution. O The test statistic has a normal distribution. State the mean and standard deviation (in KN/m²) of the test statistic. (Round your standard deviation to three decimal places.) KN/m² KN/m² mean standard deviation 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.)
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 = 67. Let u denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? Ho: μ< 1,300 H₂: μ = 1,300 O Ho: μ = 1,300 H₂: μ = 1,300 Ho: μ > 1,300 H₂: μ = 1,300 Ho: μ = 1,300 H a: μ> 1,300 ○ Ho: μ = 1,300 H₂: μ< 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 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 binomial distribution. The test statistic has a normal distribution. If X = 1,340, find the P-value. (Round your answer to four decimal places.) P-value = 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 = 15? O The test statistic has a gamma distribution. O The test statistic has a binomial distribution. The test statistic has an exponential distribution. O The test statistic has a normal distribution. State the mean and standard deviation (in KN/m²) of the test statistic. (Round your standard deviation to three decimal places.) KN/m² KN/m² mean standard deviation 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.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS