Stat1801
Probability and Statistics: Foundations of Actuarial Science
Fall 2010-2011
Chapter VIII
Hypothesis Testing
§ 8.1
Introduction
Hypothesis
A
statistical hypothesis
is an assertion or statement about the population, usually
formulated in terms of population parameters. It is denoted by
or
.
0
H
1
H
Null Hypothesis
The
null hypothesis
, denoted by
, is usually a statement about something that
0
H
has been established, or something that has an authoritative standing, or something
worth protecting.
Alternative Hypothesis
The
alternative hypothesis
, denoted by
, is usually a statement about something
1
H
that challenges the authority, or something that needs not be protected strongly.
The hypotheses are often expressed in terms of the population parameters.
However, there exists exceptional cases in
non-parametric
problems.
Example 8.1
⎩
⎨
⎧
≠
=
118
:
118
:
1
0
μ
μ
H
H
,
,
⎩
⎨
⎧
≠
=
1
:
1
:
2
1
2
0
σ
σ
H
H
⎩
⎨
⎧
≠
=
2
1
1
2
1
0
2
:
2
:
p
p
H
p
p
H
⎩
⎨
⎧
on.
distributi
normal
not
is
Population
:
on.
distributi
normal
is
Population
:
1
0
H
H
Definition
A
test
of statistical hypothesis is a procedure, based upon the observed values of
the random sample obtained, that leads to the rejection or non-rejection of the null
hypothesis
.
0
H
P.165

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