A sample of 19 joint specimens of a particular type gave a sample mean proportional limit stress of 8.42 MPa and a sample standard deviation of 0.74 MPa.(a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.) MPaInterpret this bound.With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is less than this value.With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is greater than this value. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is centered around this value.What, if any, assumptions did you make about the distribution of proportional limit stress?We must assume that the sample observations were taken from a normally distributed population.We must assume that the sample observations were taken from a uniformly distributed population. We must assume that the sample observations were taken from a chi-square distributed population.We do not need to make any assumptions.(b) Calculate and interpret a 95% lower prediction bound for proportional limit stress of a single joint of this type. (Round your answer to two decimal places.) MPaInterpret this bound.If this bound is calculated for sample after sample, in the long run, 95% of these bounds will provide a lower bound for the corresponding future values of the proportional limit stress of a single joint of this type.If this bound is calculated for sample after sample, in the long run 95% of these bounds will be centered around this value for the corresponding future values of the proportional limit stress of a single joint of this type. If this bound is calculated for sample after sample, in the long run 95% of these bounds will provide a higher bound for the corresponding future values of the proportional limit stress of a single joint of this type.You may need to use the appropriate table in the Appendix of Tables to answer this question. A sample of 19 joint specimens of a particular type gave a sample mean proportional limit stress of 8.42 MPa and a sample standard deviation of 0.74 MPa.(a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)MPaInterpret this bound.O With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is less than this value.O With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is greater than this value.O With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is centered around this value.What, if any, assumptions did you make about the distribution of proportional limit stress?O We must assume that the sample observations were taken from a normally distributed population.O We must assume that the sample observations were taken from a uniformly distributed population.O We must assume that the sample observations were taken from a chi-square distributed population.O We do not need to make any assumptions.(b) Calculate and interpret a 95% lower prediction bound for proportional limit stress of a single joint of this type. (Round your answer to two decimal places.)MPaInterpret this bound.O If this bound is calculated for sample after sample, in the long run, 95% of these bounds will provide a lower bound for the corresponding future values of the proportional limit stress of a single jointof this type.O If this bound is calculated for sample after sample, in the long run 95% of these bounds will be centered around this value for the corresponding future values of the proportional limit stress of asingle joint of this type.O If this bound is calculated for sample after sample, in the long run 95% of these bounds will provide a higher bound for the corresponding future values of the proportional limit stress of a single jointof this type.You may need to use the appropriate table in the Appendix of Tables to answer this question.

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Answered: A sample of 19 joint specimens of a…

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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A sample of 19 joint specimens of a particular type gave a sample mean proportional limit stress of 8.42 MPa and a sample standard deviation of 0.74 MPa.

(a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)
MPa

Interpret this bound.

With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is less than this value.With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is greater than this value. With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is centered around this value.

What, if any, assumptions did you make about the distribution of proportional limit stress?

We must assume that the sample observations were taken from a normally distributed population.We must assume that the sample observations were taken from a uniformly distributed population. We must assume that the sample observations were taken from a chi-square distributed population.We do not need to make any assumptions.

(b) Calculate and interpret a 95% lower prediction bound for proportional limit stress of a single joint of this type. (Round your answer to two decimal places.)
MPa

Interpret this bound.

If this bound is calculated for sample after sample, in the long run, 95% of these bounds will provide a lower bound for the corresponding future values of the proportional limit stress of a single joint of this type.If this bound is calculated for sample after sample, in the long run 95% of these bounds will be centered around this value for the corresponding future values of the proportional limit stress of a single joint of this type. If this bound is calculated for sample after sample, in the long run 95% of these bounds will provide a higher bound for the corresponding future values of the proportional limit stress of a single joint of this type.

You may need to use the appropriate table in the Appendix of Tables to answer this question.

A sample of 19 joint specimens of a particular type gave a sample mean proportional limit stress of 8.42 MPa and a sample standard deviation of 0.74 MPa.
(a) Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)
MPa
Interpret this bound.
O With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is less than this value.
O With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is greater than this value.
O With 95% confidence, we can say that the value of the true mean proportional limit stress of all such joints is centered around this value.
What, if any, assumptions did you make about the distribution of proportional limit stress?
O We must assume that the sample observations were taken from a normally distributed population.
O We must assume that the sample observations were taken from a uniformly distributed population.
O We must assume that the sample observations were taken from a chi-square distributed population.
O We do not need to make any assumptions.
(b) Calculate and interpret a 95% lower prediction bound for proportional limit stress of a single joint of this type. (Round your answer to two decimal places.)
MPa
Interpret this bound.
O If this bound is calculated for sample after sample, in the long run, 95% of these bounds will provide a lower bound for the corresponding future values of the proportional limit stress of a single joint
of this type.
O If this bound is calculated for sample after sample, in the long run 95% of these bounds will be centered around this value for the corresponding future values of the proportional limit stress of a
single joint of this type.
O If this bound is calculated for sample after sample, in the long run 95% of these bounds will provide a higher bound for the corresponding future values of the proportional limit stress of a single joint
of this type.
You may need to use the appropriate table in the Appendix of Tables to answer this question.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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