Prof. G. Jakubson
Economics 321
March 2007
Spring 2007
PRELIMINARY EXAM #1
This is a closed book exam.
You are permitted to have a calculator.
There is a formula sheet at the end of the exam
(Appendix 2), and some results that you will need to refer to in Appendix 1.
Answer the questions below in an exam book or books.
SHOW YOUR WORK
!
Be sure to label each answer, and
each part of each answer, clearly.
Neatness counts -- if I cannot read it I cannot give you credit.
Note that questions have different weights, and parts within a question may not be weighted equally.
If you get
stuck on a particular problem, skip it and move on to the next one. If you cannot remember exactly how to answer a
question, you may get partial credit for setting it up even if you don't solve it.
Read the questions carefully.
Do Parts I (q1-5) and II (q6-7) in separate bluebooks.
You have 75 minutes to complete the seven (7) questions on the exam.
Part I (Questions 1-5)
Do Parts I (q1-5) and II (q6-7) in separate bluebooks.
1.
(15 points)
In 1993, the distribution of infant mortality rates (deaths per 1000 lives births) over 131 countries
with available data was as follow:
Infant mortality
Number of countries
rate
0 to
< 10
24
10 to < 20
24
20 to < 30
14
30 to
< 50
18
50 to < 75
18
75 to < 100
16
100 to < 140
13
140 to 180
4
a.
What is the median infant mortality rate within this group of countries?
What assumption does this
calculation of the median rely upon?
b.
Give the cumulative relative frequency distribution of infant mortality rates. (Use fractions rather than
decimals to save time.)
c.
EXTRA CREDIT:
Give the expressions that you would evaluate to find the mean infant mortality rate and the
variance of infant mortality rates from these grouped data.
(Do not evaluate them, but write down these
expressions as functions of the available data.)
2.
(30 points)
Suppose you have data on a variable X.
A "standardized" variable Z is constructed by using
the following linear transformation:
Z
(X
X) / s
i
i
=
−
x
for each observation i = 1, ..., n.
a.
What is
Z
?
Economics 321, Applied Econometrics
Page 1 of 6
Preliminary Exam #1, Spring 2007
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