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Hypothesis Tests: An Introduction
Hypothesis Test about
μ
:
σ
Not Known
Hypothesis Test about a Population proportion: Large Samples
Chapter 9: Hypothesis Tests About the Mean and
Proportion
Bin Wang
bwang@jaguar1.usouthal.edu
Department of Mathematics and Statistics
University of South Alabama
Mann E6
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Hypothesis Tests: An Introduction
Hypothesis Test about
μ
:
σ
Not Known
Hypothesis Test about a Population proportion: Large Samples
Two Hypotheses
Rejection and Nonrejection Regions
Two Types of Errors
Tails of a Test
General Test Procedures
Two Hypotheses
Deﬁnition (Null hypothesis)
A null hypothesis is a statement (claim) about a population
parameter that is assumed to be true until it is declared false. A
null hypothesis is denoted by
H
0
.
Deﬁnition (Alternative hypothesis)
An alternative hypothesis is a statement (claim) about a
population parameter that is true if the null hypothesis is false. An
alternative hypothesis is denoted by
H
1
or
H
A
.
Mann E6
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Hypothesis Tests: An Introduction
Hypothesis Test about
μ
:
σ
Not Known
Hypothesis Test about a Population proportion: Large Samples
Two Hypotheses
Rejection and Nonrejection Regions
Two Types of Errors
Tails of a Test
General Test Procedures
Rejection and Nonrejection Regions
Deﬁnition (Rejection region)
Rejection region is a region in which we have enough evidence to
declare that the null hypothesis is false.
If
H
0
is declared false,
H
1
is true.
Deﬁnition (Nonrejection region)
Nonrejection region is a region in which we have no enough
evidence to declare that the null hypothesis is false.
If
H
0
is not declared false, we will assume it to be true.
Mann E6
3/34
Hypothesis Tests: An Introduction
Hypothesis Test about
μ
:
σ
Not Known
Hypothesis Test about a Population proportion: Large Samples
Two Hypotheses
Rejection and Nonrejection Regions
Two Types of Errors
Tails of a Test
General Test Procedures
Mann E6
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Notes
Notes
Notes
Notes
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View Full DocumentHypothesis Tests: An Introduction
Hypothesis Test about
μ
:
σ
Not Known
Hypothesis Test about a Population proportion: Large Samples
Two Hypotheses
Rejection and Nonrejection Regions
Two Types of Errors
Tails of a Test
General Test Procedures
Two Types of Errors
Deﬁnition (Type I Error)
A Type I error occurs when a true null hypothesis is rejected. The value
of
α
represents the probability of committing this type of error, that is,
α
=
P
(
H
0
is rejected

H
0
is true
)
The true value of
α
represents the signiﬁcance level of the test.
Deﬁnition (Type II Error)
A type II error occurs when a false null hypothesis is not rejected. The
value of
β
represents the probability of committing a Type II error. That
is,
β
=
P
(
H
0
is not rejected

H
0
is false
)
The value of 1

β
is called the power of the test. It represents the
probability of not making a Type II error.
Mann E6
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 Fall '09
 Wangs

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