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# This means that the probability to the left of z2 is

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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 &lt; Z &lt; 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 σ ME = zα/2 √ n 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.

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