Economic Statistics Exam 2
Last name:
March 31, 2009
First name:
PPID:
Section number:
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This exam contains
fifteen
short answer questions
(
worth 6 points each
)
and
three
long answer questions
(
worth 15 points each
)
. Show your work clearly to be eligible
for partial credit. In all problems where you need to make a calculation, simplify your
answer as much as convenient. In questions with multiple parts, you should respond
as if your answers to previous parts were correct.
Some PDFs:
Some probabilities:
f
(
x
)
=
1
2
!"
2
e
#
(
X
#
μ
)
2
"
2
P
[
x
!
a
]
=
e
"
#
a
f
(
x
)
=
1
u
!
!
P
[
X
]
=
x
e
!
X
!
f
(
x
)
=
!
e
"
x
P
[
X
]
=
N
!
X
!(
N
!
X
)!
p
X
(1
!
p
)
N
!
X
Short Questions
(
6 points apiece
)
1. The formal statement of a hypothesis has two parts.
What are these called, and
what does each describe?
The “null hypothesis” is the idea that we wish to test; the “alternative hypothesis” is a
formal statement of what we assume to be true if the null is false.
2. What is the formula for the minimum variance unbiased estimator of the
population variance?
s
x
2
=
1
(
N
!
1)
(
X
i
!
X
)
2
i
=
1
N
"
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View Full DocumentEcon 400 Midterm 2, page 2 of 7.
3. Each person has a
10%
chance of being left

handed. I have a class of
100
students,
and my classroom has
15
left

handed desks.
What is the chance that I have more
left

handed students than desks?
This uses the normal approximation to the binomial distribution. The number of lefties is
distributed approximately
X
~
N
(
Np
,
Np
(1
!
p
))
=
N
(10,9)
. For a normal distribution with
mean of
10
and standard deviation of
3
=
9
,
P
[
X
>
15]
=
P
[
Z
>
(15
!
10) / 3]
=
0.0478
.
4. You want to determine whether the earnings of former prison inmates differ
significantly from the earnings of the rest of the population. Construct an
80%
confidence interval for the difference in earnings between these groups:

Summary of earnings
inmate 
Mean
Std. Dev.
Freq.
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 Spring '08
 turchi
 Normal Distribution, Standard Deviation, PF, ACME corporation

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