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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:
x ± zα/2 √
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.
- Spring '08