STAT 506  Sampling Theory and Methods
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Department of Statistics
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Eberly College of Science
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Lesson 1: Introduction; Estimating Population Mean and Total under Simple Random Sampling
1.4 Confidence Intervals and the Central Limit Theorem
Submitted by gfj100 on Mon, 11/30/2009  18:30
Unit Summary
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The confidence interval for μ, τ
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Finite population Central Limit Theorem
Confidence Intervals
The idea behind confidence intervals is that it is not enough just using sample mean to estimate the
population mean. The sample mean by itself is a single point. This does not give people any idea as to how
good your estimation is of the population mean.
If we want to assess the accuracy of this estimate we will use confidence intervals which provide us with
information as to how good our estimation is.
A confidence interval, viewed before the sample is selected, is the interval which has a prespecified
probability of containing the parameter. To obtain this confidence interval you need to know the sampling
distribution of the estimate. Once we know the distribution, we can talk about confidence.
We want to be able to say something about θ, or rather
because
should be close to θ.
So the type of statement that we want to make will look like this:
Thus, we need to know the distribution of
. In certain cases the distribution of
can be stated easily.
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 Fall '08
 staff
 Statistics, Central Limit Theorem, Normal Distribution, Sampling Theory and Methods

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