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# Now lets do an example utku suleymanoglu umich

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Unformatted text preview: scuss what it means: CI for µ, Case 1: Normal Population, σ known If population has a normal distribution and σ is known, a 100(1 − α)% conﬁdence interval for µ can be constructed via: σ x ± zα/2 √ ¯ n where zα/2 is the z value such that F (z ) = 1 − α/2 or simply z value with upper tail probability of α/2. Now let’s do an example. Utku Suleymanoglu (UMich) Interval Estimation 6 / 17 Interval Estimation of Population Mean Example Suppose you have a normally distributed population with variance σ 2 = 4. You have a sample of 400 observations, whose sample average is x = 3. Let’s build a 90% conﬁdence ¯ interval for µ. If (1 − α) = 0.90, then α = 0.10 and α/2 = 0.05. What is the zα/2 ? Look up the table for upper tail probability of 0.05: F (1.645) = 0.95, 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 esti...
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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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