10/15/2008
1
STAT 2000
Sections 6.46.6
Sampling Distributions
AgrestiFranklin
Sampling Distributions
•What other distributions have we talked about?
•How do we describe distributions?
A
sampling distribution
is a probability
distribution for a statistic.
It provides
probabilities for the possible values of the
statistic.
Statistics we have studied:
,
s
Sampling Distribution of the Sample Mean,
Section 6.5 
first
Sampling Distribution of the Sample Proportion
x
x
Section 6.4 
second
We will determine shape, center and spread for
each of these sampling distributions.
We will also
use these distributions to find probabilities.
Why are sampling distributions important?
Regulating Nicotine in Cigarettes
The conditions prescribed in the FTC's 1967
announcement are the following:
1. Smoke cigarettes to a 23mm. butt length, or to
the length of the filter and overwrap plus 3mm. if
in excess of 23mm.;
2 Base results on a test of 100 cigarettes per
2. Base results on a test of 100 cigarettes per
brand, or type;
3. Cigarettes to be tested will be selected on a
random basis, as opposed to "weight selection";
Report nicotine yield to the nearest 1/10 milligram.
Tar
yield and CO concentration are also reported.
If one cigarette had been tested, and the population
was normal, we could find the probability that the
nicotine content of that cigarette was more than
1.72 milligrams (the yield in 1998).
Note, however, that 100 cigarettes are tested.
In
this case, the average is calculated, and we want to
find the probability that the SAMPLE
AVERAGE,
,
is more than 1.72 milligrams.
In order to find this probability, we will have to know
more about the distribution of the sample averages,
the
sampling distribution
of the sample mean.
x
Class Exercise:
Working in pairs, toss a die 4 times.
Record the
number of dots and calculate the average.
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We will look at the THREE different distributions
that are part of this exercise.
Population Distribution
: The distribution from
which we took our sample.
Data Distribution
: The distribution of the data
from ONE sample.
Sampling Distribution
of the Sample Mean: The
distribution of the sample averages.
Population Distribution


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_______________________________
X
123456
Shape:
Center:
Spread:
Data Distribution  One Sample






x
_______________________________
Shape:
Center:
Spread:
Sampling Distribution: Distribution of
values






x
_______________________________
1
2
3
4
5
6
x
Shape:
Center:
Spread:
Sampling Distribution of the Sample Mean
Center
: The mean of the sampling distribution of
equals the mean of the population.
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 Spring '08
 smith
 Normal Distribution, Probability, Sample Mean Center

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