Download Sampling Distributions and the CLT

Sampling Distributions and the CLT
Definition of Sampling Distribution
A sampling distribution of a sample statistic for a fixed sample size n is the
distribution of that statistic derived from every possible sample of size n for
a given population.
Sampling Distribution for a Sample Proportion
p̂
The sampling distribution for a sample proportion p̂ for sample size n is
the distribution of the p̂ 's taken from every possible sample of size n for a
given population.
Sampling Distribution for a Sample Mean
The sampling distribution for a sample mean x for sample size n is the
distribution of the x 's taken from every possible sample of size n for a given
population.
Goal of a CLT
The goal of a CLT is to describe the sampling distribution for a given
sample statistic for a given sample size.
CLT Summary
Variable Type
Sample Statistic
Required
Conditions
Conclusion:
Sampling
Distribution
Type of
sampling
When is n
Large?
Shape
Mean
Standard
Deviation
CLT for a Sample
Proportion
Categorical
CLT for a Sample
Mean
Quantitative
pˆ
x
SRS
SRS
When np ³10 and
n(1- p) ³10
Population
normal
n ³ 30
Approx. Normal
Normal
Approx. Normal
s
s
n
æ s ö
Nç m,
÷
è
nø
n
æ s ö
~ Nçm,
÷
è
nø
p
Abbreviation
p(1- p)
n
æ
p(1- p) ö
~ Nçp,
÷
n ø
è
APSI – 2010 – page 1 of 1
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