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Chapter 9
Hypothesis Testing
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View Full Document Testing vs. Estimation
±
Confidence Intervals are used to estimate an
unknown population parameter using sample
data.
±
A Hypothesis test is used when theory
suggests a particular value for an unknown
population parameter.
The question then
becomes whether the sample data is
consistent with the theory or not.
A Theory about the value of a
population parameter?
±
One popular test of ESP
uses what is called a Rhine
deck, which consists of
cards with five different
images on them.
±
The cards are put in
random order, and the
subject must guess the card
that has been drawn
without seeing it.
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View Full Document The Rhine Deck and ESP
±
The population parameter you are
investigating is the proportion of correct
answers in an infinitely long sequence of
guesses.
±
The sample statistic is the sample proportion
of correct answers in a fixed number of
guesses
The Theory
±
There is one obvious theory here: Nothing is going
on and the person is just guessing.
By guessing the
person should get 20% correct.
This is the value of
the population parameter we wish to test.
±
Given sample data, such as 25 correct in 100 trials,
the question becomes: Is this sample evidence
enough to disprove the theory that the person is just
guessing?
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View Full Document The Null Hypothesis
±
The theoretical value of the
unknown population
parameter we wish to test is
called
the null hypothesis
.
±
H
0
is the universal notation for
a null hypothesis.
±
Often the null corresponds to
the idea “nothing interesting
or unexpected is going on.”
00
0
:
In this application,
:.
2
0
Hpp
Hp
=
=
The Alternative Hypothesis
±
The alternative hypothesis comes
in three flavors
²
Less than
²
Not equal to (twosided)
²
Greater than
±
HsubA signifies the alternative
hypothesis
±
Which flavor is a matter of
judgment: What do you expect to
be true if the null is false?
0
0
0
:
:
:
A
A
A
H
pp
H
H
<
≠
>
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View Full Document ESP and the Alternative
Hypothesis
±
If you believe that ESP (if it
exists) will manifest itself in the
person getting more than 20%
correct, you’d do a greater than
test.
±
This leaves the possibility p < .20
hanging, so generally it is tossed
into the null hypothesis.
0
0
:.
2
0
2
0
2
0
2
0
A
A
Hp
=
>
≤
>
Be careful about your notation!
0
0
2
0
Correct
:1
2
:.
2
0
:7
H
Hp
H
µ
σ
=
=
=
±
Null and alternate hypotheses are
always
about
unknown population parameters; they are
never
about sample statistics.
0
0
2
0
Incorrect
2
2
0
HX
Hs
=
=
=
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View Full Document Isn’t this nitpicking?
±
Confusing sample statistics and population
parameters leads to complete nonsense.
±
The statement is a perfect example.
²
Before the sample is drawn, a sample statistic is
a random variable, and therefore can’t be equal
to a constant.
²
After the sample is drawn, the sample mean is
just a number.
No fancy statistical theory is
required to compare two known numbers.
0
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This note was uploaded on 03/01/2012 for the course ECON 371 taught by Professor Staff during the Spring '08 term at UVA.
 Spring '08
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