9.1 Hypotheses and Test Procedures
Def’n: A null hypothesis
is a claim about a population parameter that is assumed to be
true until it is declared false.
An alternative hypothesis
is a claim about a population parameter that will be true
if the null hypothesis is false.
In carrying out a test of H
0
vs. H
A
, the hypothesis H
0
is “rejected” in favour of H
A
only if
sample evidence strongly suggests that H
0
is false.
If the sample does not contain such
evidence, H
0
is “not rejected” or you “fail to reject” it.
NEVER “accept” H
0
or H
A
…for different reasons.
Ex9.1) H
0
:
μ
= 2.8
H
A
:
μ
≠
2.8
↑
↑
pop’n characteristic
hypothesized value or “claim”
Def’n: A twotailed test
has “rejection regions” in both tails.
A onetailed test
has a “rejection region” in one tail.
A lowertailed test
has the “rejection region” in the left tail.
An uppertailed test
has the “rejection region” in the right tail.
Ex9.2)
a)
H
0
:
μ
= 15
H
A
:
μ
= 15
Æ
INCORRECT
b)
H
0
:
μ
= 123
H
A
:
μ
= 125
Æ
INCORRECT
c)
H
0
:
μ
= 123
H
A
:
μ
< 123
Æ
CORRECT
d)
H
0
:
p
= 0.4
H
A
:
p
> 0.6
Æ
INCORRECT
e)
H
0
:
p
= 1.5
H
A
:
p
> 1.5
Æ
INCORRECT
f)
H
0
:
p
ˆ = 0.1
H
A
:
p
ˆ
≠
0.1
Æ
INCORRECT
TwoTailed Test
LowerTailed Test
UpperTailed Test
Sign for H
0
=
= or
≥
= or
≤
Sign for H
A
≠
<
>
“Rejection region”
In both tails
In the left tail
In the right tail
Ex9.3)
Is the mean different than
μ
0
?
H
0
:
μ
=
μ
0
H
A
:
μ
≠
μ
0
Is the mean lower than
μ
0
?
H
0
:
μ
≥
μ
0
H
A
:
μ
<
μ
0
Is the mean lower or still the same than
μ
0
?
H
0
:
μ
≤
μ
0
H
A
:
μ
>
μ
0
Is the mean higher than
μ
0
?
H
0
:
μ
≤
μ
0
H
A
:
μ
>
μ
0
Def’n: A test statistic
is the function of the sample data on which a conclusion to reject or
fail to reject H
0
is based.
For example,
Z
and
t
are test statistics.
The
p
value
is a measure of inconsistency between the hypothesized value for a
pop’n characteristic and the observed sample.
Assuming H
0
is true, the
p
value
can be
defined as the probability of obtaining a test statistic value at least as inconsistent with H
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 Winter '07
 HenrykKolacz
 Null hypothesis, Statistical hypothesis testing, H0

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