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Unformatted text preview: e zα/2 ? Look up the table
for upper tail probability of 0.05: F (0.95) = 1.645, so zα/2 = 1.645.
We have one of the components of margin of error down. What is the other? SE of the
√
mean = σ/ n = 2/20 = 0.1
Then the margin of error is 1.645 × 0.1 = 0.1645. And our conﬁdence interval estimate is
(3 − 0.1645, 3 + 0.1645) = (2.8355, 3.1645)
Now, big question: what does the conﬁdence interval mean? “The probability that µ is in
this interval is 90%”? NO! Utku Suleymanoglu (UMich) Interval Estimation 6 / 16 Interval Estimation of Population Mean Interpretation of Conﬁdence Interval Estimates Population parameter, µ, is unchanging. It is not probabilistic.
Once you build an interval with the single x at hand, µ is either inside or outside of
¯
it. You don’t know which is the case, but there is no probability to it.
So you don’t say “probability that µ is in my CI is 90%”.
Correct interpretation of CI’s are related to sampling distributions. Notice L and U
¯
are also functions of X , hence also random themselves.
We build diﬀerent CI’s with diﬀerent x ’s if we had diﬀerent samples.
¯
We had kept doing this (repeated sampling), we know that 90% of the CI’s we build
will have the correct µ in it.
That is why 100(1 − α)% is called the conﬁdence level. NOT because we have 90%
probability that µ is inside of the conﬁdence interval we just built.
But we are 90% conﬁdent 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 Suleymano...
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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
 STAFF

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