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)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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.)
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