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Economic Statistics Exam 3
Last name:
December 12, 2006
First name:
PPID:
Please sign that you abide by the honor pledge:
This exam contains
twenty
short answer questions
(
worth 4 points each
)
and
six
long answer questions
(
worth 15 points each
)
.
Please answer in the space provided; if
you need more room, indicate clearly that the answer is continued on the back of the
page.
In all problems where you need to make a calculation, simplify your answer as
much as possible.
Show your work clearly to be eligible for partial credit.
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
(
4 points apiece
)
1.
You have a small stock portfolio.
Over the past year, the returns on these stocks
were:

28
%
,

6
%
,

3
%
, 1
%
, 1
%
, 5
%
, 12
%
, 28
%
, and 43
%
.
Give the
five

number
summary
of this distribution.
Max: 43
%
75
th
:
12
%
Median: 1
%
25
th
:

3
%
Min:

28
%
2.
In general, I believe that pie charts are uninformative
(
or rather, that they are no
more informative than a list of proportions
)
.
However, I did name one “good” way
to use pie charts.
What is it?
When placed side

by

side, so that we can easily compare proportions in different groups.
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View Full Document3.
A database contains the fuel efficiency
(
in terms of miles per gallon
)
of seventeen
car models.
These values are:
18.6
19.9
20.5
32.8
19.2
20.2
20.6
36.1
19.4
20.2
20.8
36.1
19.4
20.5
25.1
39.4
43.1
Construct a box

and

whisker plot to describe this data.
The box goes from 19.9
(
the 25
th
percentile
)
to 32.8
(
the 75
th
percentile
)
, with a vertical line at
20.5
(
the median
)
.
The whiskers extend to 18.6 and 43.1.
4.
The starting salaries of economics majors are distributed with a mean of
$
35,000
and a standard deviation of
$
5,000.
With this information
(
and no additional
assumptions!
)
, calculate the fraction of salaries between
$
25,000 and
$
45,000.
According to Chebyshev’s Theorem, at least
(
1
!
1
k
2
)
fraction of observations lie within k
standard deviations of the mean.
In this problem,
$
25,000 is two standard deviations below the
mean and
$
45,000 is two standard deviations above, so at least
(
1
!
1
2
2
)
=
3
4
of observations are
within this range.
5.
On any given day, it can be sunny or rainy, and it can be cold or warm.
There is a
0.30 chance that it is rainy; there is a 0.20 chance that it is cold; and there is a 0.25
chance that it is
both
rainy and cold.
What is the probability that it is cold
or
rainy
(
or both
)
?
P
[cold or rain]
=
P
[cold]
+
P
[rain]
!
P
[cold and rain]
=
0
.
30
+
0
.
20
!
0
.
25
=
0
.
25
(
As a note, the probabilities in the problem are impossible. Oops.
)
6.
The Center for Disease Control estimates that about 1 in 300 Americans is
infected with HIV.
There is a rapid test for HIV, which is fairly accurate.
Among
people with the virus, 99 of 100 tests are positive; among people without the virus, 1
out of 200 tests results in a
(
false
)
positive.
If someone takes the test and gets a
positive result, what is the chance that he is infected with the virus?
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