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Ch. 20  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.
e.g. 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.
e.g. 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”
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This note was uploaded on 07/31/2011 for the course STAT 141 taught by Professor Paulcartledge during the Winter '10 term at University of Alberta.
 Winter '10
 PaulCartledge

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