MGEB12H3 Study Guide - Final Guide: Decision Rule, Pepperoni, Null Hypothesis
3 Jun 2018
School
Department
Course
Professor
1
ECMB12H3 Section L30
Quantitative Methods in Economics II
Summer 2001
University of Toronto at Scarborough
Dr. Yu
Final Examination
Date: Wednesday, August 14, 2001
Time allowed: Two (2) hours
Aids allowed: Calculator and two aid sheets (four 8.5”x11” pages) prepared by
student.
Notes:
• This exam consists of 14 questions in 11 pages including this cover page.
• It is the student’s responsibility to hand in all pages of this exam. Any missing page
will get zero mark.
• Show your work in each question in Part II.
• This exam is worth 40% of your course grade.
Print Last Name: Solution
Given Name(s):
Student Number:
Do not write on the space below, for markers only
Page Question Total Marks
2-4 1-10 40
4-5 11 15
6-7 12 15
8-9 13 15
10-11 14 15
Total 100
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2
Part I. Multiple Choice. 4 marks in each question. No part mark.
Circle only one answer. If there are more than one correct answer, circle the best one.
1. Suppose 45.0:
0=pH is to be tested against 45.0:
1>pH at the
α
=0.14 level
of significance where p is the probability of getting a “yes” vote in a population.
If the sample size is 200, the smallest number of “yes” votes that will cause 0
H
to be rejected is closest to
(A) 85 (B) 90 (C) 94 √ (D) 98 (E) 102
2. Candidate Jones claims that over 60% of voters are favouring him in the
upcoming election. A random sample of 2500 voters shows that 1550 of them are
favouring him. The p-value to test this claim is closest to
√ (A) 0.02 (B) 0.04 (C) 0.08 (D) 0.16 (E) 0.32
Questions 3-4. Use the following information.
A random sample of 12 observations is selected to estimate a simple regression
relationship between an independent variable X and a dependent variable Y. A
partial ANOVA table is given below.
Source SS df MS F
Regression 250
Error
Total 350
3. In testing the significance of the model, the value of the t-statistic is closest to
(A) 3 √ (B) 5 (C) 13.5 (D) 25 (E) 27.5
4. The length of a 95 percent confidence interval for the mean value of Y at the mean
value of X is closest to
(A) 2.01 (B) 2.98 (C) 3.28 √ (D) 4.02 (E) 5.96
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3
Questions 5-8. Use the following information.
A random sample 921 ,...,, XXX is selected from a normal distribution with mean
µ
and variance 2
σ
. Let ∑
=
=9
1
9
1
i
i
XX and
()
∑
=
−= 9
1
2
2
8
1
i
iXXS .
5. The probability
(
)
σµ
+>XP is closest to
√ (A) 0.0013 (B) 0.0228 (C) 0.1587 (D) 0.3413 (E) 0.9987
6. The probability
(
)
SXP +>
µ
is between
(A) 0 to 0.005 √ (B) 0.005 and 0.01 (C) 0.01 and 0.02
(D) 0.02 and 0.025 (E) 0.025 and 1
7. We wish to test 5:
0=
µ
H versus 5:
1<
µ
H using the 5% significance level.
Suppose
()
72
9
1
2=−
∑
=
i
iXX . The null hypothesis 0
H will be rejected if
(A) 5785.0−<X (B) 8595.1−<X (C) 8595.6<X
(D) 5785.10<X √ (E) 1405.3<X
8. Another independent random sample 921 ,...,, YYY is also selected from this normal
distribution and the sample mean is denoted by ∑
=
=9
1
9
1
i
i
YY . The probability
(
)
σ
>−YXP is closest to
√ (A) 0.017 (B) 0.483 (C) 0.5 (D) 0.75 (E) 0.983
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Document Summary
Calculator and two aid sheets (four 8. 5 x11 pages) prepared by student. Notes: this exam consists of 14 questions in 11 pages including this cover page. It is the student"s responsibility to hand in all pages of this exam. Solution: show your work in each question in part ii, this exam is worth 40% of your course grade. Do not write on the space below, for markers only. If there are more than one correct answer, circle the best one. =ph at the =0. 14 level of significance where p is the probability of getting a yes vote in a population. If the sample size is 200, the smallest number of yes votes that will cause. 45. 0 to be rejected is closest to (a) 85 (b) 90 (c) 94. Candidate jones claims that over 60% of voters are favouring him in the upcoming election. A random sample of 2500 voters shows that 1550 of them are favouring him.
