MGEB12H3 Study Guide - Midterm Guide: Standard Deviation, Analysis Of Variance, Confidence Interval
3 Jun 2018
School
Department
Course
Professor
1
ECMB12S Quantitative Methods in Economics II, Section L30
Division of Management
University of Toronto at Scarborough
January – May 2003
Dr. Yu
Test 2
Date: Thursday, March 20, 2003
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 20 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 (Z, t, and F 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 Mark
2-5 1-15 45
6 16 10
7 17 10
8 18 10
9 19 10
10-11 20 15
Total 100
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2
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 follow:
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: 448.3
400/21400/20
300305
// 22
2
2
21
2
1
21 =
+
−
=
+
−
=
nSnS
XX
Z
Questions 2-4. Use the following information.
Summary statistics computed for two independent samples from two normal
populations are shown as follow:
Size Mean Standard Deviation
Sample 1 13 305 20
Sample 2 10 300 21
2. In testing whether the variances of two populations are equal or not, the
acceptance region using a significance level of 5% is
(a) 080.2080.2 <<− t (b) 721.1721.1 <<− t
(c) 87.32584.0 << F √ (d) 87.32907.0 << F
(e) 07.33571.0 << F
3. In testing whether the means of the two populations are equal or not, the
acceptance region using a significance level of 5% is closest to
√ (a) 080.2080.2 <<− t (b) 721.1721.1 <<− t
(c) 87.32584.0 << F (d) 87.32907.0 << F
(e) 07.33571.0 << F
4. Assume that the population variances are equal. In testing whether the means of
two populations are equal or not, the value of the test statistic is closest to
√ (a) 0.5817 (b) 0.757 (c) 0.907 (d) 1.1025 (e) 1.28
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3
Questions 5-7. Use the following information.
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 is selected from one source and
independently random sample B is selected from the other source. Both samples
are large samples. Sample A shows that 20% of customers make purchases and
sample B shows only a 18%.
5. A 90% confidence interval for the difference in the percentages of customers who
make purchases from sources A and B is (0.005, 0.035). If there are 4000
customers in sample A, the number of customers in sample B is closest to
(a) 3012 √ (b) 3421 (c) 4000 (d) 4520 (e) 4900
6. Suppose sample A and sample B consist of 4000 customers each, a 90 percent
confidence interval for the difference in the percentages of customers who make
purchases is closest to
(a) 0.02 ±0.0275 (b) 0.02 ±0.0214 (c) 0.02 ±0.0195
(d) 0.02 ±0.0172 √ (e) 0.02 ±0.0144
7. Suppose sample A and sample B consist of 4000 customers each. 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
Questions 8-10. Use the following information.
A simple regression analysis is performed to relate maintenance expense (Y,
dollars per month) to usage (X, hours per week). A random sample of 82
observations showed an F-statistic of 10 in the ANOVA table, and the scatter plot
suggested that maintenance expense increases as usage increases. The sample
variance of Y is 100.
8. The sample correlation coefficient between X and Y is closest to
(a)
9
1 (b)
5
1 (c) 4
1 √ (d) 3
1 (e)
2
1
9. The value of MSE (Mean Squared Error) in the ANOVA table is closest to
(a) 60 (b) 70 (c) 80 √ (d) 90 (e) 100
10. If the sample variance of X is 36
1, the slope of the simple regression line is closest
to
(a) 1 (b) 5 (c) 10 (d) 15 √ (e) 20
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Document Summary
Ecmb12s quantitative methods in economics ii, section l30. Calculator and one aid sheet (two 8. 5 x11 pages) prepared by student. Notes: this test consists of 20 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 (z, t, and f 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. Summary statistics computed for two independent samples from two populations are shown as follow: 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.
