A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Please show me question of I and II

Suppose we are trying to measure some physical constant . Assume that each time we measure µ, there is a small, independent random error ~ N(0, 0²) with σ = 0.01. o (i) How many measurements do we need to construct a 99% confidence interval of length 0.01 for u? (ii) If we can only afford to make only 10 measurements, what level of confidence can we achieve for a confidence interval of length 0.01? (iii) How small doeso need to be (i.e. how precise do our measurements need to be) if we want to construct a 99% confidence interval of length 0.01 for µ from only 10 measurements? (iv) Suppose the precision of our measurements improves to o = 0.001. What is the length of a 99% confidence interval obtained from 10 measurements?
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Transcribed Image Text:Suppose we are trying to measure some physical constant . Assume that each time we measure µ, there is a small, independent random error ~ N(0, 0²) with σ = 0.01. o (i) How many measurements do we need to construct a 99% confidence interval of length 0.01 for u? (ii) If we can only afford to make only 10 measurements, what level of confidence can we achieve for a confidence interval of length 0.01? (iii) How small doeso need to be (i.e. how precise do our measurements need to be) if we want to construct a 99% confidence interval of length 0.01 for µ from only 10 measurements? (iv) Suppose the precision of our measurements improves to o = 0.001. What is the length of a 99% confidence interval obtained from 10 measurements?
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