in making a decision about a parameter
value rather then
obtaining an estimate of its value
8.2 Formulation of Hypotheses
•
A null
hypothesis
H
0
is the hypothesis against which we hope to
gather evidence. The hypothesis for which we wish to gather
supporting evidence is called the alternative hypothesises
H
a
•
One-tailed (directional) test and two-tailed test
8.3 Conclusions and Consequences for a Hypothesis Test
•
The goal of
any hypothesis-testing is to make a decision based on
sample information: whether to reject H
0
in favor of
H
a
→
we make
one of two types of error.
•
A Type I error occurs if we reject H
0
when it is true. The probability of
committing a Type I error is denoted by
α
(also called significance
level)
•
A Type II error occurs if we do not reject H
0
when it is false. The
probability of committing a Type II error is denoted by
β
.
•Contents
•[Back]

26
Chapter 8
(continued 1)
8.4 Test statistics and rejection regions
•
The test statistic
is a sample ststistic, upon which the decision
concerning the null and alternative hypotheses is based
.
•
The rejection region
is the set of
possible values of the test statistic for
which the null hypotheses will
be rejected.
•
Steps for testing hypothesis
•
Critical value =boundary value of the rejection region
8.5 Summary
8.6 Exercises
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]

27
Chapter 9. Applications of Hypothesis Testing
9.1 Diagnosing a hypothesis test
9.2 Hypothesis test about a population mean
9.3 Hypothesis test about a population proportion
9.4 Hypothesis tests about the difference between two
population means
9.5 Hypothesis tests about the difference between two
proportions
9.6 Hypothesis test about a population variance
9.7 Hypothesis test about the ratio of two
population
variances
9.8 Summary
9.9 Exercises
•[Back]
•[Contents]

28
Chapter 9
(continued 1)
9.2 Hypothesis test about a population mean
•
Large- sample test
(n>=30):
–
the sampling distribution of
is approximately normal and s is a good
approximation of
σ
.
–
Procedure for large- sample test
•
Small- sample test
:
–
Assumption: the population ha aaprox. Normal distribution.
–
Procedure for small- sample test (using t-distribution)\
9.3 Hypothesis test about a population proportion
Large- sample test
9.4 Hypothesis tests about the difference between
two population means
•
Large- sample test
:
–
Assumptions: n
1
>=30, n
2
>=30; samples are selected randomly and
independently from the populations
•
Small- sample test
•[Back
]

29
Chapter 9
(continued 2)
9.5 Hypothesis tests about the difference between two
proportions:
Assumptions, Procedure
9.6 Hypothesis test about a population variance
–
Assumption: the population has an approx. nornal distr.
–
Procudure using chi-square distribution
9.7 Hypothesis test about the ratio of two
population
variances (optional)
–
Assumptions: Populations has approx. nornal distr., random
samples are independent.