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Economic Statistics Exam 3
Last name:
December 14, 2009
First name:
PID:
Please sign that you abide by the honor pledge:
This exam contains
twenty
short answer questions (worth 6 points each) and
three
long answer questions (worth 15 points each). 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
πσ
2
e
−
(
X
−
μ
)
2
σ
2
P
[
x
≤
a
]
=
1
−
e
−
λ
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
1.
Suppose that the random variable
X
is drawn from a normal distribution with
a mean of 12 and a variance of 16. What is the probability that
X
is between 10
and 18?
2.
A researcher draws a random sample of size
N
=
9
from a normal distribution.
His sample has a mean of 52 and a standard deviation of 6. Construct a 95%
confidence interval for the population mean.
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View Full DocumentEcon 400 Midterm 3, page 2 of 9.
3.
Suppose
that
you
estimate
Y
as
a
quadratic
function
of
X
:
Y
i
=
β
0
+
1
X
i
+
2
X
i
2
+
e
i
. In Stata, you type:
. gen x2 = x^2
. reg y x x2
Source 
SS
df
MS
Number of obs =
1000
+
F(
2,
997) =
233.17
Model 
48166.9162
2
24083.4581
Prob > F
=
0.0000
Residual 
102975.057
997
103.284912
Rsquared
=
0.3187
+
Adj Rsquared =
0.3173
Total 
151141.973
999
151.293267
Root MSE
=
10.163

y 
Coef.
Std. Err.
t
P>t
[95% Conf. Interval]
+
x 
1.570586
.3091338
5.08
0.000
2.177213
.9639583
x2 
4.546693
.2165667
20.99
0.000
4.121714
4.971671
_cons 
1.91043
.397595
4.80
0.000
1.130211
2.690649

What is the estimated marginal effect of
X
on
Y
(that is,
∂
Y
∂
X
)?
4.
In the previous question, how would you test the hypothesis that
X
has no
effect at all on
Y
? Either write out your null and alternative hypotheses, or write
the Stata command(s) you would use to test it.
5.
I have an egg carton with 12 eggs; 4 are fresh, and 8 are rotten. If I select three
eggs at random from the carton, what is the chance that all three are rotten?
Econ 400 Midterm 3, page 3 of 9.
6.
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This note was uploaded on 03/19/2010 for the course ECON 400 taught by Professor Turchi during the Spring '08 term at UNC.
 Spring '08
 turchi

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