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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,
t= x −µ
s/ n has a Student’s t distribution with n-1 degrees of freedom.
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.
- Spring '08