Prof. G. Jakubson
Economics 321
March 2004
Spring 2004
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 empirical 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.
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.
As it says on the cover of
The Hitchhiker's Guide to the Galaxy
,
DON'T PANIC !
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.
You have 75 minutes to complete the nine (9) questions on the exam.
1.
(20 points)
Below are the frequency distributions of family incomes in 1988, for Caucasian families and
African-American families.
These data are adapted from the U.S. Bureau of the Census.
Class intervals
thousands of families
for family income
Caucasian
African-American
< $5,000
2,000
900
$ 5,000 to < $10,000
3,000
1,100
$10,000 to < $15,000
5,000
900
$15,000 to < $25,000
10,000
1,600
$25,000 to < $35,000
10,000
900
$35,000 to < $50,000
12,000
900
14,000
600
$50,000 or more
Total number of families
56,000
6,900
a.
In what class interval is median family income of African-American families?
Which distribution
has the higher median family income?
(You do not need to calculate median family income for Caucasian
families, but you should explain how you can tell which distribution has a higher median.)
b.
Give the cumulative relative frequency distribution
of family income of African-American families.
2.
(25 points)
Suppose you have data on a variable X.
A "standardized" variable Z is constructed by using
the following linear transformation:
x
i
i
s
/
)
x
x
(
z
−
=
for each observation i = 1, .
.., n.
a.
What is
Z
?
b.
What is s
z
?
Economics 321, Cornell University
Page 1 of 6
Prelim 1, Spring 2004
c:\…\s04pre1.doc