Please help step by step with an explanation for Program R (CS) with a final code for understanding thank you. Parameter Estimation + Confidence Interval + Margin of ErrorMeans when σ is knownProblem#223. A simple random sample of size n is drawn from a popula-tion that is normally distributed with population standarddeviation, o, known to be 13. The sample mean, x, is foundto be 108.(a) Compute the 96% confidence interval forsize, n, is 25.(b) Compute the 96% confidence interval for if the samplesize, n, is 10. How does decreasing the sample size affectthe margin of error, E?if the sample(c) Compute the 88% confidence interval for if the samplesize, n, is 25. Compare the results to those obtained inpart (a). How does decreasing the level of confidence affectthe size of the margin of error, E?(d) Could we have computed the confidence intervals inparts (a)-(c) if the population had not been normallydistributed? Why?(e) If an analysis of the sample data revealed three outliersgreater than the mean, how would this affect the confi-dence interval?(a) 102.67 113.33(b) 99.57 116.42(c) 103.96-112.04(d) Yes(e) CI will shift

Set the population standard deviation (sigma) and the sample mean (r). For part (a), compute the 96%…

Parameter Estimation + Confidence Interval + Margin of Error Means when o is known Problem#2 23. A simple random sample of size n is drawn from a popula- tion that is normally distributed with population standard deviation, o, known to be 13. The sample mean, x, is found to be 108. (a) Compute the 96% confidence interval for if the sample size, n, is 25. (b) Compute the 96% confidence interval for u if the sample size, n, is 10. How does decreasing the sample size affect the margin of error, E? (c) Compute the 88% confidence interval for if the sample size, n, is 25. Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E? (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Why? (e) If an analysis of the sample data revealed three outliers greater than the mean, how would this affect the confi- dence interval? (a) 102.67 113.33 (b) 99.57 116.42 (c) 103.96 112.04 (d) Yes (e) CI will shift

Parameter Estimation + Confidence Interval + Margin of Error Means when o is known Problem#2 23. A simple random sample of size n is drawn from a popula- tion that is normally distributed with population standard deviation, o, known to be 13. The sample mean, x, is found to be 108. (a) Compute the 96% confidence interval for if the sample size, n, is 25. (b) Compute the 96% confidence interval for u if the sample size, n, is 10. How does decreasing the sample size affect the margin of error, E? (c) Compute the 88% confidence interval for if the sample size, n, is 25. Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E? (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Why? (e) If an analysis of the sample data revealed three outliers greater than the mean, how would this affect the confi- dence interval? (a) 102.67 113.33 (b) 99.57 116.42 (c) 103.96 112.04 (d) Yes (e) CI will shift

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter12: Review Of Calculus And Probability

Section12.7: Z-transforms

Problem 3P

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Concept explainers

Random Variables

A random variable Z is a real valued function of the type Z: S → R on a sample space S. That means the function assigns a real number to every primitive event in the sample space. In other words, a random variable is a function mapping a sample space S to a set of real numbers R.

Question

Please help step by step with an explanation for Program R (CS) with a final code for understanding thank you.

Parameter Estimation + Confidence Interval + Margin of Error
Means when σ is known
Problem#2
23. A simple random sample of size n is drawn from a popula-
tion that is normally distributed with population standard
deviation, o, known to be 13. The sample mean, x, is found
to be 108.
(a) Compute the 96% confidence interval for
size, n, is 25.
(b) Compute the 96% confidence interval for if the sample
size, n, is 10. How does decreasing the sample size affect
the margin of error, E?
if the sample
(c) Compute the 88% confidence interval for if the sample
size, n, is 25. Compare the results to those obtained in
part (a). How does decreasing the level of confidence affect
the size of the margin of error, E?
(d) Could we have computed the confidence intervals in
parts (a)-(c) if the population had not been normally
distributed? Why?
(e) If an analysis of the sample data revealed three outliers
greater than the mean, how would this affect the confi-
dence interval?
(a) 102.67 113.33
(b) 99.57 116.42
(c) 103.96-112.04
(d) Yes
(e) CI will shift

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