ECON 303, EXAM 1
FALL 2008
DUE: WEDNESDAY, OCTOBER 8, 2008 at 12:40 PM
Please show your work.
There are 3 sections.
Each section carries equal weight.
If you have ANY questions, please ASK ME.
Yes, the LC HONOR CODE APPLIES
Section 1: Interpreting Information
1)
A few years ago the news magazine
The Economist
listed some of the stranger
explanations used in the past to predict presidential election outcomes. These included
whether or not the hemlines of women’s skirts went up or down, stock market
performances, baseball World Series wins by an American League team, etc. Thinking
about this problem more seriously, you decide to analyze whether or not the presidential
candidate for a certain party did better if his party controlled the house. Accordingly you
collect data from 34 past presidential elections. You think of these data as comprising a
population which you want to describe, rather than a sample from which you want to
infer behavior of a larger population. You generate the accompanying table:
Joint Distribution of Presidential Party Affiliation and Party Control of House of
Representatives, 18601996
Democratic Control
of House (
0
Y
=
)
Republican Control
of House (
1
Y
=
)
Total
Democratic
President (
0
X
=
)
0.412
0.030
0.441
Republican
President (
1
X
=
)
0.176
0.382
0.559
Total
0.588
0.412
1.00
(a)
Interpret one of the joint probabilities and one of the marginal probabilities.
(b)
Compute
( )
E X
. How does this differ from
(

0)
E X Y
=
? Explain.
.
(c)
If you picked one of the Republican presidents at random, what is the probability that
during his term the Democrats had control of the House?
(d)
What would the joint distribution look like under independence? Check your results by
calculating the two conditional distributions and compare these to the marginal
distribution.
1
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Math SAT scores (
Y
) are normally distributed with a mean of 500 and a standard
deviation of 100. An evening school advertises that it can improve students’ scores by
roughly a third of a standard deviation, or 30 points, if they attend a course which runs
over several weeks. (A similar claim is made for attending a verbal SAT course.) The
statistician for a consumer protection agency suspects that the courses are not effective.
She views the situation as follows:
0
:
500
Y
H
μ
=
vs.
1
:
530
Y
H
=
.
()a
Sketch the two distributions under the null hypothesis and the alternative
hypothesis.
()b
The consumer protection agency wants to evaluate this claim by sending
50 students to attend classes. One of the students becomes sick during the course and
drops out. What is the distribution of the average score of the remaining 49 students
under the null, and under the alternative hypothesis?
()c
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 Econometrics, Regression Analysis, Null hypothesis, Statistical hypothesis testing, Human height, Francis Galton, Forint Yen Dollar Baht Crown Ruble Crown Crown Peso Franc Shekel Yuan Rand Franc Zloty Mark Dollar Dollar Dollar Real Dollar Dollar Peso

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