Download topic #6: sampling

ECON 4630
ECON 5630
TOPIC #6: SAMPLING
I.
Introduction and Motivation
A.
General
B.
Why Is Sampling Necessary?
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II.
Probability Sampling Methods
A.
Probability vs. Non-Probability Sampling
B.
Types of Probability Sampling
1.
Simple Random Sampling
2.
Systematic Random Sampling
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3.
Stratified Random Sampling
4.
Stratified Cluster Sampling
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III.
Sampling Error and Sampling Distributions
A.
Definition: sampling error is the difference between a sample estimate and the
corresponding population parameter.
B.
Sampling Distributions
Imagine drawing samples from a given population over and over again. If we
calculate X each time, we’ll slowly put together a probability distribution of the
sample means. Here’s an extended example:
Executive’s Name
Snow
Years of
Service
20
Tolson
22
Kraft
26
Irwin
24
Jones
28
What’s the population mean?
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Now suppose we draw samples of 2 from this population. There are
5!
 10 different possibilities for samples:
2!(5  2)!
Sample
Snow
Tolson
Snow
Kraft
Snow
Irwin
Snow
Jones
Tolson
Kraft
Tolson
Irwin
Tolson
Jones
Kraft
Irwin
Kraft
Jones
Irwin
Jones
Sample Mean
In histogram form:
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Points to note:
What is the mean of the means? How does it compare with the population mean?
What is the shape of the distributions of sample means?
IV.
The Central Limit Theorem:
In repeated random samples of a particular size, the sampling distribution of the
sample means is distributed approximately normal, with mean =  and standard
deviation of
V.

n
. (If  is unknown, we use our estimate of it, S)
Excel Commands
To generate random numbers between 0 and 1, use =RAND(). To generate random numbers
between a and b, use =RANDBETWEEN(a,b).
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NOTES:
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