Name:__________________________
Economics 2900
Final Exam
Spring, 2010
Thursday, April 22nd 2010
The use of a simple calculator is allowed.
Question # 1
Question # 2
Question # 3
Question # 4
Question # 5
Question # 6
10 marks
20 marks (part a 15 marks. part b 5 marks)
15 marks (part a 10 marks. part b 5 marks)
20 marks
15 marks (part a 10 marks. part b 10 marks)
20 marks
Total
100 marks
Question #1
You are the manager of a fast-food restaurant. You want to determine whether the population
mean waiting time to place an order has changed in the past month from its previous population
mean value of 4.5 minutes. From past experience, you can assume that the population is
normally distributed with a population standard deviation of 1.2 minutes. You select a sample of
25 orders during a one-hour period. The sample mean is 5.1 minutes. Has the population mean
waiting time to place an order has changed in the past month from its previous population mean
value of 4.5 minutes. Use alpha = .08
Question # 2
Calculate the probability of a type 2 error for your test in question # 1, if the true mean
waiting time is 5 minutes.
Explain in words the meaning of a type 1 and type 2 error as it relates to this problem.
Question # 3
Robots are being used with increasing frequency on production lines to perform
monotonous tasks. To determine whether a robot welder should replace human welders
in producing an automobiles, an experiment was performed. The time for the robot to
complete a series of welds was found to be 38 seconds. A random sample of welds from
20 workers was taken and the mean time to complete the same series of welds was also
found to be 38 seconds ( the same as the robots time) with a variance of 27.47. The
robots time did not vary. An analysis of the production line revealed that if the variance
exceeds 17 seconds2, there will be problems. Should the humans be replaced? Use
alpha = .10
B) The union president insists that the company be 99% confident the robots are better
than the human welders before they are replaced. Would this change your decision
above? Explain.
Question # 4
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 # 5
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 .06 significance level. Also report exactly how confident she can
be in the test results.
B
Generate a 94% Confidence interval Estimator for the true difference in
popularity. Does this interval agree with your test result?
Question # 6
The human resources (HR) director for a large company that produces highly technical
industrial instrumentation devices is interested in using regression modeling to help in
making recruiting decisions concerning sales managers. The company has 45 sales regions,
each headed by a sales manager. Many of the sales managers have degrees in electrical
engineering, and due to the technical nature of the product line, several company officials
believe that only applicants with degrees in electrical engineering should be considered. At
the time of their application, candidates are asked to take the Strong-Campbell Interest
Inventory Test and the Wonderlic Personnel Test. Due to the time and money involved with
the testing, some discussion has taken place about dropping one or both of the tests. To start,
the HR director gathered information on each of the 45 current sales managers, including
years of selling experience, electrical engineering background, and the scores from both the
Wonderlic and Strong-Campbell tests. The dependent variable was “sales index” score,
which is the ratio of the regions’ actual sales divided by the target sales. The target values are
constructed each year by upper management, in consultation with the sales managers, and are
based on past performance and market potential within each region. The variables included
are
Sales – Ratio of yearly sales divided by the target sales value for that region. The
target values were mutually agreed-upon “realistic expectations”.
Wonder – Score from the Wonderlic Personnel Test. The higher the score, the
higher the applicant’s perceived ability to manage.
SC -- Score on the Strong-Campbell Interest Inventory Test. The higher the
score, the higher the applicant’s perceived interest in sales.
Experience – Number of years of selling experience prior to becoming a sales
manager.
Engineer – Dummy variable that equals 1 if the sales manager has a degree in
electrical engineering and 0 otherwise.
An example of the first few lines of the data are listed below, the regression results are on the
following page.
Manager #
1
2
3
.
.
.
44
45
Sales
96
90
113
.
.
.
101
95
Wonder
27
35
30
.
.
.
33
27
SC
42
46
55
.
.
.
50
54
Experience
5
8
8
.
.
.
9
4
Engineer
1
1
0
.
.
.
0
1
Yes
Yes
No
.
.
.
No
Yes
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.77021321
R Square
0.59322838
Adjusted R Square 0.55255122
Standard Error
11.7420288
Observations
45
ANOVA
df
Regression
Residual
Total
4
40
44
SS
8042.99042
5515.00958
13558
Intercept
Wonder
SC
Experience
Engineer
Coefficients
25.7683409
-0.0134104
1.35141645
0.16815638
7.27470818
Standard
Error
13.95370291
0.404976302
0.19470923
0.528712892
4.101130081
MS
2010.748
137.8752
F
14.583819
t Stat
1.846703
-0.03311
6.94069
0.318049
1.77383
P-value
0.0721979
0.9737483
2.268E-08
0.7521027
0.0837043
What can the HR director tell from the regression printout
Significance F
1.97883E-07