MGEB12H3 Study Guide - Final Guide: Bulgarian Lev, Analysis Of Variance, Decision Rule
3 Jun 2018
School
Department
Course
Professor
ECMB12S-L30 Quantitative Methods in Economics II
Division of Management and Economics
University of Toronto at Scarborough
Winter 2007 Dr. Yu
Final Examination
Date: Wednesday April 25, 2007
Time allowed: Two (2) hours
Aids allowed: Calculator, Regression Handout and one aid sheet (two 8.5”x11”
pages) prepared by student.
Notes:
• This exam consists of 20 questions in 13 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.
• 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 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 Max Mark
2-4 1-15 45
5 16 7
6 17 8
7-8 18 10
9-10 19 15
11-13 20 15
Total 100
1
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.
1. A 95% confidence interval for the population mean
µ
is (20.5, 25.5). In testing
the hypothesis 22:
0=
µ
H versus 22:
≠
µ
a
H, which one of the following
statements is most correct? Denote the significance level by
α
.
(a) Reject at
0
H
α
=0.05.
(b) Reject at
0
H
α
=0.01.
(c) The p-value is less than 0.05.
√ (d) The p-value is greater than 0.05.
(e) The power of the test is 0.95.
2. A simple regression line of Y on X is Y = 10 – 2X. If X increases by 1 unit, we
expect the value of Y to
√ (a) decrease by 2 units (b) decrease by 8 units
(c) increase by 2 units (d) increase by 8 units
(e) decrease by 1 unit.
3. In a hypothesis test 2.0:
0
=
pH versus , where p is the population
proportion, a researcher specifies a p-value of 0.05. The sample proportion was
equal to 0.25. The sample size is closest to
2.0: >pHa
(a) 64 √ (b) 174 (c) 246 (d) 363 (e) 472
4. The one-sample t statistic for testing 0:
0
=
µ
Hrsus ve 0>:
µ
a
H from a
sample of n=15 observations has the value t =1.82. Which one of the following
statements is true?
(a) Reject
at
0
H05.0=
α
(b) Accept at
0
H01.0
=
α
(c) Accept at
0
H001.0=
α
√ (d) All of the above are true
(e) None of the above is true
5. In a survey that measures the coffee consumption of 36 truck drivers we find a
sample average of 11.5 and standard deviation of 9.0 both measured in cups per
day. A researcher wishes to test whether average consumption is greater than 10
cups per day. In performing the hypothesis test the researcher specifies the
significance level at 5%. If the true population mean was actually 15 cups per day
then the probability of a Type II error is closest to
(a) 0.0456 (b) 0.1287 (c) 0.2456 √ (d) 0.9543 (e) 0.9959
2
6. An automobile manufacturer lists the fuel efficiency for a particular model at 30
miles per gallon (mpg). A consumer group conducts 64 mileage tests and
discovers a sample mean of 29.55 mpg and a sample standard deviation of 1.8
mpg. A hypothesis test is conducted to evaluate if the manufacturer is overstating
the fuel efficiency. The significance level at which the null hypothesis will not be
rejected is closest to
(a) 0.001 (b) 0.015 √ (c) 0.0228 (d) 0.0325 (e) 0.10
7. Let
1
X be the mean of a random sample of size 100 from a population with mean
20 and standard deviation 12; 2
X be the mean of a random sample of size 100
from a population with mean 20 and standard deviation 5. Assume that 1
X and
2
X are independent. The probability
(
)
2
21 ≤− XXP is closest to
(a) 0.0618 (b) 0.4382 (c) 0.5618 (d) 0.7142 √ (e) 0.9382
8. A random sample is drawn from a normal population with mean
µ
and standard
deviation
σ
=5. A 95 percent confidence interval for
µ
is (29.9, 30.3). If the
sample data are used to test 30:
0
=
µ
H versus 30:
1>
µ
H, the smallest value
of
α
that will be rejected is closest to
0
H
(a) 0.01 (b) 0.05 (c) 0.102 (d) 0.125 √ (e) 0.1635
Questions 9 – 11, we wish to test the hypothesis 5:
0
=
µ
H versus 5:<
µ
a
H.
9. Which one of the following statements is true?
(a) If we reject at
0
H05.0
=
α
, we must also reject at
0
H01.0
=
α
.
(b) If we reject at
0
H05.0
=
α
, we must accept at
0
H01.0
=
α
.
√ (c) If we accept at
0
H05.0
=
α
, we must also accept at
0
H01.0=
α
.
(d) If we accept at
0
H05.0
=
α
, we must reject at
0
H01.0
=
α
.
(e) None of the above is true.
10. Which one of the following statements is true?
(a) If the p-value is less than 0.1, we reject at
0
H05.0
=
α
.
√ (b) If the p-value is less than 0.05, we reject at
0
H1.0
=
α
.
(c) If we reject at
0
H1.0
=
α
, a 90% confidence interval for
µ
can be (3,6).
(d) If we accept at
0
H1.0
=
α
, a 90% confidence interval for
µ
can be (6,9).
(e) None of the above is true.
11. A random sample of 400 shows a mean of 4.5 with a standard deviation of 4. The
p-value is closest to
√ (a) 0.0062 (b) 0.0524 (c) 0.1032 (d) 0.1432 (e) 0.1820
3
