NAME:______________________
I.D. # : ______________________
ECONOMICS 2900
Economics and Business Statistics
Summer Session 1 2005
FINAL EXAMINATION
Thursday June 23rd
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 (20 points)
Workers in a large plant are expected to complete a particular task, on average, in 60 seconds or
less. The production manager wants to develop a test to determine if the average time is
something other than 60 seconds. To examine the issue she watches eight workers perform the
task and measures their times. The times, which are assumed to be normally distributed, are
shown below. Assume the population standard deviation is 4 seconds. Use alpha = .05
58 , 53 , 63 , 62 , 57 , 55 , 53 , 55
Sample mean = 57
Sample standard deviation =3.82
What is the probability of a type 2 error in the above test if the workers true average time of completion is
59 seconds. Explain what this means to the manager.
Question # 2 (20 points)
A survey of 1,500 Canadians reveals that 945 believe that there is too much violence on television. In
a survey of 1,500 Americans, 810 believe that there is too much television violence.
A.
Can we infer at the 99% significance level that the proportion of Canadians and Americans
who believe that there is too much violence on television differ?
(5 marks)
B.
Estimate with 99% confidence the difference in the proportion of Canadians and Americans
who believe that there is too much violence on television.
(5 marks)
C. Briefly explain how the interval estimate in Question B confirms your answer to question A.
(3 marks)
D. Calculate the pvalue for the test in question A.
(5 marks)
E. Which country has the highest number of people who believe there is too much violence on
TV?
(2 marks)
Question # 3 (15 marks)
Because of the rising costs of industrial accidents, many chemical, mining, and
manufacturing firms have instituted safety courses. Employees are encouraged to take these
courses designed to heighten safety awareness. A company is trying to decide which one of
two courses to institute. To help make a decision eight employees take course 1 and another
eight take course 2. Each employee takes a test, which is graded out of a possible 25. The
safety test results are shown below. Assume that the scores are normally distributed. Do these
data provide sufficient evidence at the 5% level of significance to infer that the marks from
course 1 are lower than those of course 2?
Course 1
Course 2
Course 1
Course 2
Mean Std. dev
17.25 2.60
19.13 3.00
14
20
21
18
17
22
14
15
17
23
19
21
20
19
16
15
Question #4 (15 points)
Automobile insurance appraisers examine cars that have been involved in accidental
collisions to assess the cost of repairs. An insurance executive is concerned that different
appraisers produce significantly different assessments. In an experiment 10 cars that have
recently been involved in accidents were shown to two appraisers. Each assessed the
estimated repair costs. These results are shown below. Can the executive conclude at the 5%
significance level that the appraisers differ in their assessments?
Car
1
2
3
4
5
6
7
8
9
10
Appraiser 1
Appraiser 2
Mean Variance
816
153560
762
105507
Appraiser 1
1650
360
640
1010
890
750
440
1210
520
690
Appraiser 2
1400
380
600
920
930
650
410
1080
480
770
Question # 5 (15 marks)
A government official is visiting a dentist’s office to inspect the x-ray machine. If the machine emits too
little radiation, clear photographs cannot be obtained. However, too much radiation can be harmful to the
patient. Government regulations specify an average emission of 60 millirads with standard deviation of 12
millirads. After examining the machine, the inspector is satisfied that the average emission is still 60
millirads. However there is wear on certain mechanical parts. To test the variability, the inspector takes a
random sample of 30 x-ray emissions and finds the sample standard deviation to be 15 millirads. Should
the inspector shut down the dentist’s x-ray machine for violating code? The inspector must be 99% certain
there is a problem before acting.
Question # 6 (15 marks)
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
(9 points)
DF
3
96
99
SS
MS
17098 699.3
21553 224.5
38651
F
2.865
What information can the professor gain from this regression model?
SIGNIF-F
.0432
(2 points)
Based on the regression output, which students tend to do the best? Which students tend to do
the worst?
(4 points)
What is Multicollinearity? Could it be a problem in this model?
Bonus
(2 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?