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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 o² and a fixed; (ii) as o? is increased, keeping n and a fixed; (iii) as a is decreased, keeping n and o² 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?

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 o² and a fixed; (ii) as o? is increased, keeping n and a fixed; (iii) as a is decreased, keeping n and o² 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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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? 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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