### Confidence Interval Calculation for Normally Distributed PopulationA simple random sample of size \( n \) is drawn from a population that is normally distributed. The sample mean, \( \bar{x} \), is found to be 115, and the sample standard deviation, \( s \), is 10.#### Tasks:**(a)** Construct a 96% confidence interval about the population mean \( \mu \) if the sample size, \( n \), is 27.**(b)** Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 17.**(c)** Construct a 95% confidence interval about \( \mu \) if the sample size, \( n \), is 27.**(d)** Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?*Click the icon to view the table of areas under the t-distribution.*---#### Calculation Box**(a)** Construct a 96% confidence interval about \( \mu \) if the sample size, \( n \), is 27.- Lower bound: [Input Box]- Upper bound: [Input Box]*(Use ascending order. Round to one decimal place as needed.)*

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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 simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 19.4, and the sample standard deviation, s, is found to be 4.3. (a) Construct a 95% confidence interval about μ if the sample size, n, is 31. (b) Construct a 95% confidence interval about μ if the sample size, n, is 63. How does increasing the sample size affect the margin of error, E? (c) Construct a 98% confidence interval about μ if the sample size, n, is 31.How does increasing the level of confidence affect the size of the margin of error, E? (d) If the sample size is 21, what conditions must be satisfied to compute the confidence interval?
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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 108, and the sample standard deviation, s, is found to be 10. (a) Construct a 96% confidence interval about µ if the sample size, n, is 13. (b) Construct a 96% confidence interval about µ if the sample size, n, is 29. (c) Construct a 99% confidence interval about μ if the sample size, n, is 13. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? FClick the icon to view the table of areas under the t-distribution. (a) Construct a 96% confidence interval about μ if the sample size, n, is 13. Lower bound: Upper bound: (Use ascending order. Round to one decimal place as needed.)
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