1
Hypothesis Tests with Means
of Samples
Introducing the Central Limit Theorem
(CLT)
Sampling Distributions
•
Z-distribution
– A comparison distribution of
individual scores
.
– We had the population and want to know how ONE
score fits on that distribution.
•
How does that ONE person fall WRT the mean in terms of
standard deviations?
•
Distribution of Means
:
– The distribution of the means of a very large number
of samples
of the same size
taken from the same
population of individuals
The Central Limit Theorem
(CLT)
“
Given a population with mean μ and variance
σ
2
,
the sampling distribution of the mean (the
distribution of sample means) will have
1.
a mean equal to μ (i.e., μ
X
=μ)
2.
a variance (
σ
2
X
) equal to
σ
2
/n and
3.
a standard deviation (
σ
X
) equal to
σ
/(n)
1/2
The distribution will approach the normal distribution as
n, the sample size, increases.”
The Central Limit Theorem (CLT)
•
The foundation for many statistical procedures.
•
Backbone for
parametric statistics:
– Tests that require assumptions about the shape
(including the variance) of the population distribution.

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The Central Limit Theorem (CLT)
The Central Limit Theorem (CLT)
•

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