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Chapter 9 Statistical Inference: Significance Tests
about Hypotheses (Hypothesis Testing)
9.1: What are the steps for performing a
Significance Test?
In this section we will introduce the language and
steps of significance testing. The procedures will be
addressed in later sections of Chapter 9.
Basics of Significance Testing
1.
A statement is made about a population
parameter.
2.
A claim is made that this statement is incorrect.
3.
Evidence (sample data) is collected in order to
test the claim.
4.
The data are analyzed in order to support or
refute the claim.
Example: A car manufacturer advertises a mean gas
mileage of 26 mpg. A consumer group claims that the
mean gas mileage is less than 26 mpg. A sample of
33 cars is taken and the sample mean for these 33
cars is 25.2 mpg.
Significance testing
is a procedure, based on sample
evidence and probability, used to test claims
regarding a characteristic of one or more populations.
We use sample data to test hypotheses.
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The Five Steps of a Significance Test:
1. Assumptions
2. Hypotheses
3. Test Statistic
4. Pvalue
5. Conclusion
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1. Assumptions
– each type of test will have certain
assumptions that we need to check (ex. is the sample size
large enough?)
2. Hypotheses
Each significance test has two hypotheses about a
population parameter:
the null and alternative hypotheses.
The null hypothesis
, denoted
H
0
(read “Hnaught”) is a
statement to be tested.
The null hypothesis is assumed true
until evidence indicates otherwise.
In this chapter, it will
be a statement regarding the value of a population
parameter.
In our car example, the null hypothesis is
H
0
:
μ
= 26 mpg
This is the statement made by the car manufacturer that we
have to accept as true before we test the claim.
The alternative hypothesis
, denoted
H
A
, is a claim to be
tested.
Generally, this is a statement that says the
population parameter has a value different, in some way,
from the value given in the null hypothesis. In experiments,
we are usually trying to find evidence for the alternative
hypothesis.
In our car example, the alternative hypothesis is
H
A
:
μ
< 26 mpg
This is the claim made by the consumer group, that the
mileage is less than what the car manufacturer stated.
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There are three ways to set up the null and alternative
hypotheses.
1.
Less than test (lefttailed test)
H
0
: parameter = some value
H
A
: parameter < some value
Example: A car manufacturer advertises a mean gas
mileage of 26 mpg. A consumer group claims that the mean
gas mileage is less than 26 mpg.
2.
Greater than test (righttailed test)
H
0
: parameter = some value
H
A
: parameter > some value
Example: A newspaper states that a candidate will receive
46% of the votes in an upcoming election. An analyst
believes the percentage will be higher than 46%.
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This note was uploaded on 09/10/2011 for the course STAT 2000 taught by Professor Smith during the Spring '08 term at University of Georgia Athens.
 Spring '08
 smith
 Statistics

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