STAT 409
Homework #9
Fall 2009
(due Friday, October 30, by 4:00 p.m.)
From the textbook:
8.216
9.14
9.16
9.17
9.110
9.112
7.
Let
X
1
, X
2
, … , X
25
be a random sample from a
N
(
μ
, 100
)
population,
and suppose the null hypothesis
H
0
:
μ
= 100
is to be tested.
a)
If the alternative hypothesis is
H
1
:
μ
> 100,
compute the power of the
appropriate test at
μ
= 101
and at
μ
= 102.
Use
α
= 0.05.
b)
If the alternative hypothesis is
H
1
:
μ
≠
100,
compute the power of the
appropriate test at
μ
= 101
and at
μ
= 102.
Use
α
= 0.05.
c)
For the test in (a) compute the pvalue associated with
X = 103.5.
d)
For the test in (b) compute the pvalue associated with
X = 103.5.
8.
Let
X
1
, X
2
, … , X
12
be a random sample of size
n
=12
from a Poisson distribution
with mean
λ
.
That is,
P
(
X
1
=
k
) =
!
λ
λ
k
e
k

⋅
,
k
= 0, 1, 2, 3, … .
Consider the test
H
0
:
λ
=
1
/
2
vs.
H
1
:
λ
<
1
/
2
.
The rejection region is given by
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 Spring '11
 Stepanov
 Null hypothesis, Alex, Statistical hypothesis testing, Statistical significance

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