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Unformatted text preview: − zα/2 σ/ n and U = X + zα/2 σ/ n
Utku Suleymanoglu (UMich) Interval Estimation 4 / 17 Interval Estimation of Population Mean zα/2 Deﬁnition
zα/2 is the z-value such that it has a right tail probability of α/2. This means that the
probability to the left of zα/2 is the cumulative probability. So we are looking for a z such
that F (zα/2 ) = 1 − α/2.
P (−zα/2 < Z < zα/2 ) = 1 − α 1−α
α/2 −zα/2 α/2
0 zα/2 z Example: If α = 0.05, α/2 = 0.025. So we are interested in zα/2 = z0.025 . It is a value
such that F (z0.025 ) = 1 − 0.025 = 0.975. Do an inverse look up on the z-table to
calculate F −1 (0.975) = 1.96. So z0.025 = 1.96.
Utku Suleymanoglu (UMich) Interval Estimation 5 / 17 Interval Estimation of Population Mean We ﬁgured out the lower and upper bounds of the 100(1 − α)% conﬁdence interval.
Notice that they are in the format (as promised) x ± ME .
Margin of error in this case is
ME = zα/2 √
Let’s summarize this result before we di...
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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