Q6. (a) A manufacturer of light bulbs advertises that, on average, its long-life bulb will last for more than5,000 hours. Assume that the lifetime of a randomly selected bulb of this type has a standarddeviation of 40o hours. A statistician took a random sample of 100o bulbs and measured, foreach bulb, the amount of time until the bulb burned out. The sample mean is 5,065 hours.Find a 95% confidence interval for the expected number of hours a randomly selected bulb ofthis type will last.(b) The statistician has drawn another sample of size n. However, the information about the samplemean is lost after obtaining a 1 – a confidence interval for the expected number of hours arandomly selected bulb of this type will last, which is [5, 030, 5, 070].(i) Find the sample mean.(ii) If the statistician would like to obtain a 90% confidence interval for the expected numberof hours a randomly selected bulb of this type will last and keep the maximum deviationfrom the sample mean to be 50 hours, what should be the minimum value of n?(iii) If the sample of size 1,000 is obtained and the statistician would like to obtain a 99% con-fidence interval for the expected number of hours a randomly selected bulb of this typewill last, what is the width of the interval?(iv) If the statistician has obtained the sample with size 3o0 and eventually agree with the lightbulbs manufacturer's claim, what is the maximum confidence coefficient the statisticianapplied?(c) The statistician found that the assumption on the standard deviation is incorrect. Therefore,the standard deviation is now an unknown. Find a 95% confidence interval for the expectednumber of hours a randomly selected bulb of this type will last if(i) the sample size, sample mean, the second sample moment are 100, 5,065 hours and 25814225respectively.(ii) the statistician took a random sample with size 10,000 and found out that the sample meanand the sample standard deviation are 5,065 and 400 hours respectively.

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Answered: 6. (a) Amanufacturer of light bulbs…

6. (a) Amanufacturer of light bulbs advertises that, c 5,000 hours. Assume that the lifetime of a ram deviation of 400 hours. A statistician took a each bulb, the amount of time until the bull

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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