Suppose we are trying to measure some physical constant . Assume that each time w easure µ, there is a small, independent random error ~ N(0, 0²) with o = 0.01. (i) How many measurements do we need to construct a 99% confidence interval of lengt 0.01 for u? (ii) If we can only afford to make only 10 measurements, what level of confidence can w achieve for a confidence interval of length 0.01?

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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?
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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