Consider a confidence interval, with confidence coefficient 1 - a, for the mean of a normaldistribution with known variance o?, based on a random sample of n observations. How doesthe 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 thatthe error in the estimated mean lifetime of such components will not exceed (i) 15 hours, (ii) 20hours?

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Answered: Consider a confidence interval, with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Consider a confidence interval, with confidence coefficient 1-a, for the mean of a normal distribution with known variance o2, 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 o2 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?

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