Economic Statistics Exam 1
Last name:
February 17, 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.
Formulas:
P
[
X
]
=
N
!
X
!(
N
!
X
)!
p
X
(1
!
p
)
N
!
X
P
[
X
]
=
e
!
μ
X
X
!
Short Questions
(
6 points apiece
)
1. Suppose that overall,
20%
of people have blond hair, and
25%
of people have blue
eyes, but
60%
of the population has neither blond hair nor blue eyes. Are these two
events independent?
(
Explain.
)
The
events
are
independent
if
P
["not blond" and "not blue"]
=
P
["not blond"]
!
P
["not blue"]
.
In
this
problem,
P
["not blond"]
!
P
["not blue"]
=
!
P
["blond"])
"
!
P
["blue"])
=
!
0.20)
"
!
0.25)
=
(0.80)
!
(0.75)
=
0.60
.
Since this
is the same as
P
["not blond" and "not blue"]
, the events
are
independent.
2. In the previous problem, what is the probability that a person has blond hair or
blue eyes
(
or both
)
?
One solution technique: the “complement” of being “blond, blue

eyed, or both” is “neither blond
nor blue

eyed”. The probability of this event is
1
!
0.60
=
0.40
.
3. How do we determine the length of the whiskers in a box

and

whisker plot?
The whiskers could extend as far as
1.5
!
(
IQR
)
from the 25th and 75th percentiles, though they
actually end at the nearest datapoint within this interval.
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4. According to the National Weather Service, Chapel Hill has
2.7
snowy days per
year, on average. What is the probability that we have three or more?
This
should
be
modeled
using
the
Poisson
distribution:
P
[
X
]
=
e
!
2.7
2.7
X
X
!
.
P
[
X
>
3]
=
1
!
P
[
X
"
2]
=
1
!
(
P
[0]
+
P
[1]
+
P
[2])
.
Evaluate
these
for
the
Poisson
distribution.
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 Spring '08
 turchi
 Standard Deviation, Variance, chance, Blond hair, mean weekly earnings

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