MGEB12H3 Study Guide - Final Guide: Normal Distribution, Dependent And Independent Variables, Decision Rule
3 Jun 2018
School
Department
Course
Professor
1
ECMB12H3 Section L30
Quantitative Methods in Economics II
Winter 2002
University of Toronto at Scarborough Dr. Yu
Final Examination
Date: Tuesday, April 30, 2002
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 19 questions in 10 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
2-6 1-15 45
6 16 10
7 17 15
8 18 15
9-10 19 15
Total 100
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. A manufacturer claims that his tires last at least 40,000 miles. A random sample
of 25 tires reveals that the mean life of the tires is 40,250 miles, with a standard
deviation of 387 miles. The test statistic for the claim is closest to
(A) –0.65 √ (B) 3.23 (E) 2.5 (D) 0.65 (E) –3.23
Questions 2-4. Use the following information.
A buyer wishes to test if the proportion of defective items in a shipment is over
20% or not. The hypotheses are 2.0:
0≤pH and 2.0:
1>pH .
2. Suppose the buyer selects a random sample of 400 items and finds that 92 are
defective. The p-value of the test is closest to
(A) 0.05
√(B) 0.0668 (C) 0.1587 (D) 0.3413 (E) 0.4332
3. Suppose the buyer selects another random sample of 400 items, the smallest
number of defective items in the sample that will cause 0
H to be rejected at 10%
significance level is closest to
(A) 88 √ (B) 91 (C) 94 (D) 97 (E) 100
4. Suppose the buyer selects a third random sample and finds that a 95% confidence
interval for the proportion of defective items in a shipment is (0.1216, 0.2784).
Based on this information, the test statistic for testing 0
H verses 1
H is closest to
(A) –1.645 (B) -1.96 √ (C) 0 (D) 1.645 (E) 1.96
3
Question 5-6. Use the following information.
A random sample of 400 households from a large community was selected to
estimate the mean electricity use per household during February 2001. Another
random sample of 400 households was selected, independent of the first, to
estimate the mean electricity use during February 2002. The sample results (in
kilowatt hours) were as follows:
Year Sample Size Mean Std Dev
2001 1 400 1300 200
2002 2 400 1330 210
5. A 90% confidence interval for the difference in mean electricity use between the
two years is closest to
(A) 42.2830 ±− (B) 6142.2530 ±− √ (C) 8525.2330 ±−
(D) 3213.2430 ±− (E) 785.3330 ±−
6. To test if the mean electricity use per household has changed between the two
years, the p-value is closest to
(A) 0.0192 (B) 0.0152 (C) 0.05 (D) 0.0673 √ (E) 0.0384
Questions 7-8. Use the following information.
Suppose the mean weekly income of students working in Toronto is
µ
with a
standard deviation of
σ
. Two independent random samples, each of size 50, is
selected to estimate
µ
. Denote the sample means by 1
X and 2
X.
7. The probability
(
)
σ
4.0
21 >− XXP is closest to
√(A) 0.0228 (B) 0.0062 (C) 0.4772 (D) 0.4938 (E) 0.6145
8. If
σ
=30, which one of the following has approximately a standard normal
distribution?
(A)
()
21
2
1XX − (B)
()
21
3
1XX − (C)
()
21
4
1XX −
(D)
()
21
5
1XX − √ (E)
()
21
6
1XX −
Document Summary
Calculator and two aid sheets (four 8. 5 x11 pages) prepared by student. Notes: this exam consists of 19 questions in 10 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. A manufacturer claims that his tires last at least 40,000 miles. A random sample of 25 tires reveals that the mean life of the tires is 40,250 miles, with a standard deviation of 387 miles. The test statistic for the claim is closest to. Use the following information. (e) 2. 5 (d) 0. 65 (e) 3. 23. A buyer wishes to test if the proportion of defective items in a shipment is over.
