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Consider a confidence interval, with confidence coefficient 1-a, for the mean of a normal distribution with known variance o?, based on a random sample of n observations. How does the width of the interval change (i) as n is increased, keeping o? and a fixed; (ii) as o is increased, keeping n and a fixed; (iii) as a is decreased, keeping n and o? fixed?

Consider a confidence interval, with confidence coefficient 1-a, for the mean of a normal distribution with known variance o?, based on a random sample of n observations. How does the width of the interval change (i) as n is increased, keeping o? and a fixed; (ii) as o is increased, keeping n and a fixed; (iii) as a is decreased, keeping n and o? fixed?

MATLAB: An Introduction with Applications
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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Statistics and probability
Consider a confidence interval, with confidence coefficient 1 - a, for the mean of a normal distribution with known variance o?, based on a random sample of n observations. How does the width of the interval change (i) as n is increased, keeping o? and a fixed; (ii) as o? is increased, keeping n and a fixed; (iii) as a is decreased, keeping n and o? fixed? The standard deviation of the lifetime of a certain type of electrical component is 144 hours. How large a sample of the components must be taken to be (a) 95%, (b) 99% confident that the error in the estimated mean lifetime of such components will not exceed (i) 15 hours, (ii) 20 hours?
Transcribed Image Text:Consider a confidence interval, with confidence coefficient 1 - a, for the mean of a normal distribution with known variance o?, based on a random sample of n observations. How does the width of the interval change (i) as n is increased, keeping o? and a fixed; (ii) as o? is increased, keeping n and a fixed; (iii) as a is decreased, keeping n and o? fixed? The standard deviation of the lifetime of a certain type of electrical component is 144 hours. How large a sample of the components must be taken to be (a) 95%, (b) 99% confident that the error in the estimated mean lifetime of such components will not exceed (i) 15 hours, (ii) 20 hours?
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