MGEB12H3 Study Guide - Midterm Guide: Summary Statistics, Statistical Hypothesis Testing, Confidence Interval
3 Jun 2018
School
Department
Course
Professor
1
ECMB12H3S Section L30
Quantitative Methods in Economics II
Division of Management of Economics
University of Toronto at Scarborough
Summer 2002 Dr. Yu
Test 2
Date: Thursday, August 1, 2002
Time allowed: Two (2) hours
Aids allowed: Calculator and one aid sheet (two 8.5”x11” pages) prepared by
student.
Notes:
• This test consists of 19 questions in 11 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 are provided separately. Do not hand in the tables. Only hand in
your test papers.
• Show your work in each question in Part II.
• This test is worth 30% 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
2-6 1-15 45
7 16 10
8 17 15
9-10 18 15
11 19 15
Total 100
2
Part I. Multiple Choice. 3 points in each question. No part mark.
Circle only one answer. If there are more than one correct answer, circle the best one.
Questions 1-3. Use the information in the following paragraph.
Are Japanese managers more motivated than American managers? A randomly
selected group of each were administered an Attitudes Test (AT), where higher
AT scores indicate more motivation. The AT scores from this sample are
summarized as follows:
American Japanese
Sample Size 200 100
Mean AT score 65 70
Standard Deviation 20 10
Denote the average AT scores of American and Japanese managers by a
µ
and
j
µ
respectively.
1. To determine if the average AT score of American managers are significantly
lower than the average AT score of Japanese managers, the null and alternative
hypotheses are
(A) 0:
0<− ja
H
µ
µ
, 0: ≥− jaa
H
µ
µ
(B) 0:
0≤− ja
H
µ
µ
, 0: >− jaa
H
µ
µ
√ (C) 0:
0=− ja
H
µ
µ
, 0: <− jaa
H
µ
µ
(D) 0:
0=− ja
H
µ
µ
, 0: >− jaa
H
µ
µ
(E) None of the above
2. The test statistic in question 1 is closest to
(A) –6.9 (B) –4.75 √ (C) –2.89 (D) 2.89 (E) 4.75
3. Suppose
α
=0.05. Which one of the following statements is true?
(A) The probability of a Type II error,
β
, must be equal to 0.95.
√ (B) Reject 0
H at
α
=0.05. (C) Accept 0
H at
α
=0.05.
(D) Cannot make a conclusion. (E) None of the above is true.
3
Questions 4 –6. Use the information in the following paragraph.
In order to compare the means of two populations, independent random samples
of 400 observations are selected from each population, with the following sample
results:
Sample 1 Sample 2
Mean 5,275 5,240
Standard Deviation 150 200
Denote the population means by 1
µ
and 2
µ
, respectively.
4. To test the hypotheses 25: 210 =−
µ
µ
H against 25: 21 ≠−
µ
µ
a
H, the test
statistic is
(A) Z = –2.8 (B) Z = 2.8 (C) t = -2.8 (D) t = 2.8
√ (E) none of the above
5. A 95% confidence interval for 21
µ
µ
− is
(A) 35 ±1.645(12.5) (B) 35 ±2.33(12.5) √ (C) 35 ±1.96(12.5)
(D) 35 ±3.12(12.5) (E) none of the above
6. What is the conclusion using the significance level
α
=0.05?
(A) Reject
0
H. √(B) Accept 0
H.
(C) Cannot draw conclusion (D) All of the above are possible.
(E) None of the above is possible.
Document Summary
Calculator and one aid sheet (two 8. 5 x11 pages) prepared by student. Notes: this test consists of 19 questions in 11 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 are provided separately. Solution: show your work in each question in part ii, this test is worth 30% 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. A randomly selected group of each were administered an attitudes test (at), where higher. The at scores from this sample are summarized as follows: Denote the average at scores of american and japanese managers by j respectively. a and. To determine if the average at score of american managers are significantly lower than the average at score of japanese managers, the null and alternative hypotheses are (a)
