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# How realistic is that is known not really we almost

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Unformatted text preview: nﬁdent that our interval contains the µ, because 90% of CIs built this way will contain it. At this point, I should draw a graph for you explaining the random sampling of CIs. Utku Suleymanoglu (UMich) Interval Estimation 8 / 17 Interval Estimation of Population Mean Case 2: Normally distributed population, σ unknown We keep talking about unknown population parameters: µ is unknown, we are building an interval estimate for it. How realistic is that σ is known. Not really: we almost never know what σ is. So what do we do? We can use s , sample standard deviation, instead. We can do this, but need a modiﬁcation to make it work. It turns out the sampling distribution of x is not normal if you use s instead of σ . ¯ Sampling Distribution of x with unknown σ ¯ If x is the sample mean of a sample drawn from a population with N (µ, σ 2 ) distribution, ¯ then t= x −µ ¯ √ s/ n has a Student’s t distribution with n-1 degrees of freedom. 2 2 Here sx = sn is the estimate for the sampling variance. So sx = ¯ ¯...
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## This note was uploaded on 03/17/2014 for the course ECON 404 taught by Professor Staff during the Spring '08 term at University of Michigan.

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