MGEB12H3S – L01, L30, L60
Quantitative Methods in Economics II
Friday March 21, 2014
Last Name (Print) __Solution____________________
Time allowed: Two (2) hours
Aids allowed: Any Calculator
One aid sheet (two 8.5”x11” pages) prepared by student.
This test consists of 22 questions in 12 pages including this cover page.
It is the student’s responsibility to hand in all pages of this test. Any missing
page will get zero mark.
Statistical tables (Z, t, Chi Square, F) tables are provided.
Show your work in each question in Part II.
This test is worth 25% of your course grade.
Turn to the last page, enter your name and student number again.
The University of Toronto's Code of Behaviour on Academic Matters applies to all University of
Toronto Scarborough students. The Code prohibits all forms of academic dishonesty including, but
not limited to, cheating, plagiarism, and the use of unauthorized aids. Students violating the Code
may be subject to penalties up to and including suspension or expulsion from the University.
Management, 1265 Military Trail, Toronto, ON, M1C 1A4, Canada 1
www.utsc.utoronto.ca/mgmt Part I. Multiple Choice. 3 marks in each question. No part mark.
Circle only one answer. If there are more than one correct answer, circle the best one.
1. Summary statistics computed for two independent samples from two populations are shown as
Size Mean Standard Deviation
Sample 1 400 305 20
Sample 2 400 300 21
An analyst wishes to test whether the means of two populations are equal or not. The value of
the test statistic is closest to
(a) 0.45 (b) 1.45 (c) 2.45 √ (d) 3.45 (e) 4.45
Solution: Z X1 X 2 305 300 3.448
2 2 2 2
S1/n 1 S /2 2 20 /400 21 /400
2. Let y 0 x1 be a regression model with one independent variable, and let be the
correlation between x and y. Which one of the following statements is false?
(a) If the F value in the ANOVA table is less than 1, the model is not significant.
(b) Testing H : 0 is equivalent to testingH : 0 .
0 1 0
(c) The point estimator b always has the same sign as the sample correlation coefficient r.
(d) To test the significance of the model, we must assume that the error has a normal
distribution with mean 0 and variance .
√ (e) The estimated regression equation of y on x is always the same as that of x on y.
3. Let y 0 1 be a regression model with one independent variable. To obtain the sample
regression coefficient b1using the method of least squares, which one of the following statements
(a) b1 is a random variable and 1 is a constant.
(b) yi y 0
(c) yi yi 0
√ (d) yi y is a minimum
(e) yi yi is a minimum
2 4. The correlation coefficient from the n pairs of data x1, 1 , x2, y2,..., n , nmay be affected
when each x , y is replaced by which of the following?
(a) xic, y ic (b) xic, y ic (c) cxi,cyi, c 0
(d) yi,xi √ (e) xi, i
Questions 5–6, a management recruiter wants to estimate a simple linear regression relationship
between X (number of years on a job) and Y (salary in $000) in hotel management. A random
sample of 18 observations gives the following summary statistics.
Variable Mean Deviation
X 5 3
Y 60 5
The sample correlation coefficient is r 0.6.
5. For every year of experience, the expected increase of salary is closest to
(a) less than $500 √(b) $1,000 (c) $1,500 (d) $2,000 (e) over $2,000
6. The estimated equation of the regression line is
√(a) Y 55 X (b) Y 5 60X (c) Y 60 5X
(d) Y 5 3X (e) Y 3 5X
A sample of 17 residential home sales in a city is used to fit a straight-line regression model
relating the sale price Y to the square feet of living space X. The resulting least squares
equation is Y 30,000 70X . The standard deviation of X is 100 square feet, and the
standard deviation of Y is $8,000.
7. The coefficient of determination r is equal to
1 7 49
(a) 0.7 (b) (c) √(d) (e) none of these
8 8 64
8. For a residential home with a living space of 1,000 square feet, the estimated sale price is
√(a) $40,000 (b) $70,000 (c) $90,000 (d) $120,000 (e) $150,000
9. Suppose an analyst wishes to create a simple regression model using the same sample data of
17 observations, with X as the dependent variable and Y as the independent variable. The slope
of the resulting regression equation is
1 7 7
(a) √(b) (c) (d) 70 (e) none of these
70 640 8
3 Questions 10–11.
Two independent random samples are selected to test if alcohol consumption in 1995 is
significantly higher than that in 2000. The sample results are summarized below.
Sample Consumption (litres)
Year Size Average Std Dev
1995 100 18 4
2000 100 16 3
10. To test if alcohol consumption in 1995 is significantly higher than that in 2000, the value of test
statistic is closest to
(a) 2 √(b) 4 (c) 6 (d) 8 (e) 10
11. At 5% level of significance, the conclusion in question 10 is
√(a) Alcohol consumption in 1995 is significantly higher than that in 2000.
(b) Alcohol consumption in 1995 is not significantly higher than that in 2000.
(c) Alcohol consumption in 1995 does not differ significantly than that in 2000.
(d) Alcohol consumption in 1995 differs significantly than that in 2000.
(e) none of these
A company wishes to estimate Sales Volumes (Y in $10,000) from Advertising Expenditure (X
in $10,000). A simple regression analysis from a random sample of 10 observations is results
the following partial ANOVA table.
Source SS df MS F
The company assumes a positive relationship between Sales Volume and Advertising
12. To test the significance of the model, the value of the t-test is closest to
(a) 1.96 √ (b) 3.7712 (c) 14.22 (d) 44.31 (e) 52.14
13. The correlation coefficient between Sales Volume and Advertising Expenditure is equal to
(a) 0.49 (b) 0.7 (c) 0.64 √ (d) 0.8 (e) none of these
4 Questions 14–15, a telemarketing company obtains customer names and telephone numbers from two
sources. To determine if the percentages of customers who make purchases are the same from
both sources, random sample A of size 4000 customers is selected from one source and
independently random sample B of size 4000 customers is selected from the other source.
Sample A shows that 20% of customers make purchases and sample B shows only a 18%.
14. A 90 percent confidence interval for the difference in the percentages of customers who make
purchases is closest to
(a) 0.020.0275 (b) 0.0 0.0214 (c) 0.0 0.0195
(d) 0.020.0172 √ (e) 0.0 0.0144
15. To test if the percentages of customers who make purchases are the same from both sources,
the p-value is closest to
(a) 0.005 (b) 0.0113 √ (c) 0.0226 (d) 0.0312 (e) 0.05
5 Questions 16–17, a market research firm published the following summary statistics for the population
of university students regarding their working status in the years of 2001 and 2002. In 2001,
50% of the students worked. In 2002, 52% of the students worked. Among the students who
worked, the following population statistics are given:
Year Mean Std Dev
2001 $190 $50
2002 $200 $50
16. A random sample of 400 students (no matter they worked or not) is selected from year 2001,
and independently a random sample of 400 students (no matter they worked or not) is selected
from year 2002. What is the probability that the percent of students working from the sample
of 2001 is higher than the percent of students working from the sample in 2002?
(a) 0.1 (b) 0.2 √ (c) 0.3 (d) 0.4 (e) 0.5
p1 1 0.5 0.5 0.25
Solution: p1~ N p,1 n N .5, 400 N .5, 400 ,
p2 2 0.52 0.48 0.2496
p2~ N p, 2 N .52, N .52,
n2 400 400
p q p q 0.250.2496 0.4996
p1 p 2 N p 1 , 2 1 1 2 2 N 0.02, N 0.02,
n1 n2 400 400
P p 1 p 2 P p 1p 20 P Z 0 0.02 P Z 0.5659 0.2843
17. A random sample of 100 students is selected from the students who worked in 2001, and
independently a random sample of 100 students is selected from the students who worked in
2002. What is the probability that the average weekly income from the sample of 2001 is
higher than the average weekly income from the sample in 2002?
(a) 0.01 (b) 0.02 (c) 0.04 (d) 0.06 √ (e) 0.08
Solution: X 1 N 19, 100 N 190,25 ,X 2 N 20, 100 N 200,25
X 1 X ~2N 10,50 ,
P X X 0 P Z 0 10 P Z 1.4142 0.0793
1 2 50