NAME:______________________
I.D. # : ______________________
ECONOMICS 2900
Economics and Business Statistics
Summer Session #1 2006
FINAL EXAMINATION
Monday June 26th , 2006
Weight 45%
NOTE : You have 3 hours to complete the exam, budget your time accordingly. Please answer all questions on this
exam booklet. Calculators used must not have the ability to program alphabetic characters (whole words or
sentences) GOOD LUCK
** Please do not mark the tables **
Question # 1
A politician has commissioned a survey of blue-collar and white-collar employees
in her constituency. The survey reveals that 286 out of 542 blue-collar workers
intend to vote for her in the next election whereas 428 out of 955 white-collar
workers intend to vote for her. Is the politician more popular with blue collar
workers? Use .01 significance level. Also report exactly how confident she can
be in the test results.
Question # 2
In testing the hypotheses, H 0 :   950 vs. H1 :   950 , a random sample of 25
light bulbs is drawn from a normal population whose standard deviation is 200.
Find The Probability of a type two error given that   1000 and   0.10.
Question #3
As a safety measure, wood paneling is made as nonflammable as possible. A wood product
manufacturer would like to make its product less flammable by coating it with a special new
chemical solution. However, because of the chemical’s cost, it will not be used unless it can be
shown to improve the product. As an experiment, six different types of wood paneling are selected. Each piece is split into two halves, with one half being treated with the chemical solu-tion.
Each half is then placed over an open flame, and the number of seconds until the panel bursts into
flame is recorded. The results are exhibited below. Do these data provide sufficient evidence at the
5% significance level to conclude that the chemical solution is effective?
Panel Type
1
2
3
4
5
6
Treated
Untreated
73
52
47
81
66
79
70
53
41
72
60
70
Treated
x1  66.3
2
s1  199.87
Untreated
x2  61
s 22  149.6
Question # 4
The irradiation of food to destroy bacteria is a growing phenomenon. In order to
determine which one of two methods of irradiation is best, a scientist took a
random sample of 100 one- pound packages of minced meat and subjected 50 of
them to irradiation method 1 and the remaining 50 to irradiation method 2. The
bacteria count was measured and the following statistics were computed. Which
irradiation method would you recommend as more effective in reducing the
average bacteria count? You must be at least 95% confident in your
recommendation.
Method 1
x1  86
Method 2
x2  98
s12  324
s 22  841
Question # 5
The speed limits on highways are based to some extent on the variability of reaction
times of drivers. The highway department assumes that the variability of drivers’
reaction times is  2  0.022 sec 2 . A critic of the department’s policies argues that
the variance is somewhat larger than this value. In a random sample of 100
drivers’ reaction times the following sample statistics were calculated: Average
reaction time = 0.536 seconds with a sample variance of .035 seconds2 Can we
conclude at the 1% significance level that the critic is correct?
Question # 6 (points)
A professor of economics wanted to develop a multiple regression model to predict the students’ grades in
her fourth-year economics course. She decides that the two most important factors are the student’s grade
point average in the first three years and the student’s major. She proposes the model
y = β0 + β1x1 + β2x2 + β3x3 + ε
where
y
x1
x2
x3
=
=
=
=
=
=
fourth-year economics course mark (out of 100)
G.P.A. in first three years (range 0 to 12)
1 if student’s major is economics
0 if not
1 if student’s major is finance
0 if not
The computer output (based on 100 students) appears below.
THE REGRESSION EQUATION IS
Y = 9.14 + 6.73X1 + 10.42X2 + 5.16X3
PREDICTOR
CONSTANT
X1
X2
X3
COEF
9.14
6.73
10.42
5.16
STDEV
7.10
1.91
4.16
3.93
S = 15.0
R-SQ = 44.2%
T-RATIO
1.29
3.52
2.50
1.31
PVALUE
.2000
.0003
.3600
.0440
ANALYSIS OF VARIANCE
SOURCE
REGRESSION
ERROR
TOTAL
(8 points)
DF
3
96
99
SS
MS
17098 699.3
21553 224.5
38651
F
2.865
SIGNIF-F
.0432
What information can the professor gain from this regression model?
(2 points)
Based on the regression output, which students tend to do the best? Which students tend
to do the worst?
(2 points)
What is Multicollinearity? Could it be a problem in this model?
(3 points)
The professor notices that 2 of the p-values on the printout are clearly wrong. Which two
are they and how does she know they are wrong?
Bonus Question:
what is five plus five divided by four plus six?