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Chapter 9: Statistical Inference: Significance Tests About Hypotheses
Steps for Performing a Significance Test
Significance Test:
A
significance test
is a method of using data to summarize the evidence about a
hypothesis. A
significance test
about a hypothesis has
five steps.
1)
Assumptions
2) Hypotheses
3) Test Statistic
4) Pvalue
5) Conclusion
Step 1 :
Assumptions
h
A (significance) test assumes that the data production used randomization
h
Other assumptions may include:
•
Assumptions about the sample size or about the shape of the population distribution
Step 2 :
Hypotheses
h
A
hypothesis
is a statement about a population, usually of the form that a certain parameter takes a
particular numerical value or falls in a certain range of values
h
The main goal in many research studies is to check whether the data support certain hypotheses
h
Each significance test has two hypotheses:
•
The
null hypothesis
is a statement that the parameter takes a particular value.
It has a single
parameter value. The symbol H
o
denotes null hypothesis. This always has equality “=” sign.
Ex:
H
0
: p = 0.72
H
0
: μ = 42.3
•
The
alternative
hypothesis
states that the parameter falls in some alternative range of values.
The
symbol H
a
denotes alternative hypothesis. The alternative hypothesis should express what the
researcher hopes to show. This always has one of “>”, “<”, or “
≠
” signs.
Ex:
H
a
: p < 0.47
H
a
: μ
≠
42
H
a
: μ > 3.45
x
The hypotheses should be formulated before viewing or analyzing the data!
Step 3:
Test Statistic
h
A
test statistic
describes how far the point estimate falls from the parameter value given in the null
hypothesis
h
We use the test statistic to assess the evidence against the null hypothesis by giving a probability, the
PValue.
Step 4:
Pvalue
Alternative Hypothesis
Pvalue
h
To interpret a test statistic value, we use a probability summary of
the evidence
against
the null hypothesis, H
o
•
First, we presume that H
o
is true
•
Next, we consider the sampling distribution from which the test
statistic comes
•
We summarize how far out in the tail of
this sampling
distribution the test statistic falls
h
We summarize how far out in the tail the test statistic falls by the
tail probability of that value and values even more extreme
•
This probability is called a
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This note was uploaded on 08/04/2011 for the course MATH 2300 taught by Professor Staff during the Spring '08 term at Texas Tech.
 Spring '08
 Staff
 Statistics

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