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Tests of Significance
The second inference method discussed in Chapter
14 is called tests of significance
.
When we conduct these tests, we’re going to have
some claim about our population, and we’re going
to see if the data supports or refutes that claim.
1
Chapter 14
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View Full Document Tests of Significance
Example: I claim that I make 80% of my field goal
kicks in football.
You do not believe me, so you ask me to go to the
stadium and kick 20 field goals.
I only make 8 out of the 20 field goals.
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Chapter 14
Tests of Significance
If you use the BIN(20, 0.8) distribution, the
probability I would make 8 or fewer field goals is
only about 0.0001.
If my claim is true, I would make 8 field goals or
less once in 10,000 tries.
This should convince you that my initial claim is not
true.
3
Chapter 14
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View Full Document In short: An outcome that would rarely happen if a
claim was true is good evidence that the claim is
not true
.
For our tests of significance, we will think along
these lines (and use the assumptions we have
talked about).
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Chapter 14
Stating Hypotheses
Null Hypothesis, H
0
Stating Hypotheses
Null Hypothesis, H
0
Definition
:
The initial claim tested by a statistical
test is called the null hypothesis
. This is typically
denoted as “H
o
”.
Example
:
In a court trial, the rule of thumb is
“innocent until proven guilty.” Thus, the null
hypothesis for a trial is “The person is innocent.”
5
Chapter 14
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6
•
The statement being tested in a
statistical test is called the
null
hypothesis
.
•
The test is designed to assess the
strength of evidence against the null
hypothesis.
•
Usually the null hypothesis is a
statement of “no effect” or “no
difference”, or it is a statement of
equality.
Stating Hypotheses
Null Hypothesis, H
0
Tests of Significance
When performing a hypothesis test, we assume
that the null hypothesis is true until we have
sufficient evidence against it.
The null hypothesis is the claim that a test of
significance is trying to disprove
(like my free throw
shooting).
Along with the null hypothesis, there will be another
claim which we are trying to prove
.
This claim is
called the alternative hypothesis
(denoted using
“H
a
”).
7
Chapter 14
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8
•
The statement we are trying to find evidence for
is called the
alternative hypothesis
.
•
Usually the alternative hypothesis is a
statement of “there is an effect” or “there is a
difference”, or it is a statement of inequality.
•
The alternative hypothesis should express
the hopes or suspicions we bring to the
data.
It is cheating to first look at the data
and then frame H
a
to fit what the data show.
Stating Hypotheses
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This note was uploaded on 09/23/2011 for the course STAT 2053 taught by Professor Staff during the Fall '08 term at Oklahoma State.
 Fall '08
 staff

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