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Midterm Examination I
Econ 103, Statistics for Economists
February 11, 2013
You will have 70 minutes to complete
this exam. Graphing calculators, notes,
and textbooks are not permitted.
I pledge that, in taking and preparing for this exam, I have abided by the
University of Pennsylvania’s Code of Academic Integrity. I am aware that
any violations of the code will result in a failing grade for this course.
Name:
Student ID #:
Signature:
Question:
1
2
3
4
5
6
7
8
9
Total
Points:
10
10
15
20
20
10
15
20
20
140
Score:
Instructions:
Answer all questions in the space provided, continuing on the back of the
page if you run out of space.
Show your work for full credit but be aware that writing
down irrelevant information will not gain you points. Be sure to sign the academic integrity
statement above and to write your name and student ID number on
each page
in the space
provided. Make sure that you have all pages of the exam before starting.
Warning:
If you continue writing after we call time, even if this is only to fill in your
name, fifteen points will be deducted from your final score. In addition, one point will be
deducted for each page on which you do not write your name and student ID.


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Econ 103
Midterm I, Page 2 of 9
February 11, 2013
1. (10 points) A study conducted at the University of Missouri-Columbia (“Mizzou”) found
that students who had a fake ID were more likely to engage in underage drinking while
at college. Suppose we were to give fake IDs to a randomly selected group of Mizzou
freshmen. Based only on the evidence given in this question, do you think this would
substantially increase the fraction of these students who drink underage? Explain why
or why not.
Solution:
There are many possible correct answers: the point is to use what we’ve
learned in this course about observational data and confounding to construct an
argument. Here is one possibility:
No – the causality probably runs in reverse: students who plan to do a
lot of underage drinking obtain fake IDs
expressly for this purpose
.
In
contrast, students who do not plan to engage in underage drinking have
no need of a fake ID and hence wouldn’t bother to obtain them. If we
gave fake IDs to teetotalers, they’d never use them. If we gave them to
hardened alcoholics, they’d already have one. The only students whom
this experiment might impact are those who are constrained in their
underage drinking by an inability to obtain a fake ID. Given the many
opportunities to drink underage on or near a college campus that
do not
require a fake ID, it is very unlikely that this constraint binds for many
students.
2. (10 points) Let
A
and
B
be two mutually exclusive events, where both
P
(
A
) and
P
(
B
)
are strictly greater than zero.
Are
A
and
B
independent?
Explain your answer and
provide a proof. You may use any results we derived in class without proving them but
be sure to name the results you use for full credit.
Solution:
For any two events, the Addition Rule gives,
P
(
A
B
)=
P
(
A
)+
P
(
B
)
-
P
(
A
B
)
but for mutually exclusive events,
P
(
A
B
)=
P
(
A
)+
P
(
B
)
by the third Axiom of Probability.
Combining these,
P
(
A
B
) = 0.
Two events
A
and
B
are independent if and only if
P
(
A
B
)=
P
(
A
)
P
(
B
).
But we know
that
P
(
A
)
>
0 and
P
(
B
)
>
0 so,
P
(
A
)
P
(
B
)
>
0. Since
P
(
A
B
) = 0 it follows
Name:
Student ID #:


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