∙
Asymmetric rules are sometimes preferred when testing hypotheses
about a parameter that must be strictly postive:
0.
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EXAMPLE
: Suppose in a
Normal
,1
population, we want to test
H
0
:
≤
0 against
H
1
:
0. We can obtain a random sample of size
of size
n
. We have an unbiased estimator of
,
X
̄
. It seems reasonable to
base the rejection rule on how large
X
̄
is.
∙
Let
x
̄
denote the average for the actual data we observe.
∙
If we get
x
̄
≤
0, that is no evidence against
H
0
:
≤
0.
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