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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 Stepanov

Click to edit the document details