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Midterm

MGEB12H3 Study Guide - Midterm Guide: Academic Dishonesty, Scantron Corporation, HeteroscedasticityExam


Department
Economics for Management Studies
Course Code
MGEB12H3
Professor
ATA
Study Guide
Midterm

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MGEB12 Quantitative Methods in Economics-II
Winter 2019
Test-2 (Solutions)
Instructor: A. Mazaheri
Instructions: This is a closed book test. A formula sheet is attached. You are allowed the use
of a calculator.
Write your full name and your student ID # on both this test book as well as the
Scantron paper.
You have 105 Minutes.
Notes: If you write with pencil, you will not be able to ask for regrade.
Good Luck!
Last
Name:
First
Name:
ID
FOR MARKERS ONLY:
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.
MC
Q#1
Q#2
Total
Marks Earned
Maximum Marks
Possible 64 16 20 100

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Page 2 of 40
Part A (Long Questions)
Question-1 (16 Points) Answer the following two separate parts:
Males and females were asked about what they would do if they received a $100 bill by
mail, addressed to their neighbor, but wrongly delivered to them. Would they return it to
their neighbor? The results are shown below.
Male Female
n1 = 69 n2 = 131
Yes, would return = 52 Yes, would return = 120
We are interested in determining if the “female” proportion of returning the bill is 5%
more than that of “males”.
a) [6 Points] First setup the hypothesis, then find the p-value of the test. In a maximum
of three sentences interpret the p-value and make a conclusion (inference).
Solution:
:
:
=120
131 = 0.916,
=52
69 = 0.754
:=5%
:5%
 =(
)()
1
1
=(0.916 0.754)0.05
0.916(10.916)
131 0.754(10.754)
69 1.963
= 2[PZ > 1.963)] 5%
The p-value is around 5% which indicate a strong (to moderate) evidence to reject
the null. There is strong to moderate evidence in favor of rejecting null. 5% more
Females return the bill!

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Page 3 of 40
b (10 points) A study on the time UTSC students spend playing sports each weak is done
and data are collected and summarized in the following. (Note: Both populations are
assumed to be normally distributed.)
Male
Female
Sample size
n1 = 31
n2 = 21
Sample mean (hours)
= 5
= 4.6
Sample standard deviation
S1 = 0.912
S2 = 1.1
b1(5 Points) Test at 5% if these two populations have similar variances. (Make sure to set
up the null and alternative hypothesis before you perform your test)
Solution:
2
1
2
20
:
σσ
=H
vs.
2
2
2
11
#:
σσ
H
, =1.1
0.912= 1.455
Rejection region: F > F2.5%, 20, 30 = 2.2
Conclusion: Cannot reject the null hypothesis. Cannot conclude at 5% that the variances
are different.
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