ISyE2028A, Fall 2010
Solutions to Quiz 7 (version A & B)
Version A:
1.
Let
1
,
,
m
X
X
be a random sample from a normal distribution with variance
2
1
1
, let
,
,
n
Y
Y
be
another random sample (independent of the
' )
i
X
s
from a normal distribution with variance
2
2
2
2
1
2
, and let
and
S
S
denote the two sample variances. Which of the following statement is not true?
A.
The random variable
2
2
2
2
1
1
2
2
(
/
) /(
/
)
F
S
S
has an
F
distribution with parameters
1
2
1 and
1
m
n
B.
The random variables
2
2
2
2
1
1
2
2
(
1)
/
and (
1)
/
m
S
n
S
each have a
t
distribution with
m
‐
1 and
n
‐
1
degrees of freedom, respectively.
C.
The hypothesis
2
2
1
2
:
o
H
is rejected if the ratio of the sample variances differs by too much
from 1.
D.
In testing
2
2
2
2
1
2
1
2
:
versus
:
,
o
a
H
H
the rejection region for a level
,
1.
1
test is
.
m
n
f
F
ANSWER
: B
2.
Let
1
20
,
,
X
X
be a random sample from a normal distribution with variance
2
1
1
25
, let
,
,
Y
Y
be
another random sample (independent of the
' )
i
X
s
from a normal distribution with variance
2
2
2
2
1
2
, and let
and
S
S
denote the two sample variances. Which of the following statement is not
true in testing
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 Fall '07
 SHIM
 AirTrain Newark, rejection region, A. B. C. D

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