Department of Management Sciences
Faculty of Engineering
University of Waterloo
MSci 609 Quantitative data Analysis for Management Sciences
Winter 2011
Assignment 3 (Due March 29, 2011)
Points to consider:
•
Include a title page as a separate sheet, and write on it your name, student number, and email
address.
Work on the assignment independently.
•
Please state all your assumptions and show all your work. Generous partial credit will be given if the
reasoning is correct, even if the solution is not. However, none will be given for unsubstantiated
claims, even if you provide perfectly correct answer.
•
Please do not ask for informal assessment of your work, i.e. do not ask for an assessment of whether
you were on the right track on any particular problem.
•
Assignments should be dropped in the drop
‐
box in CPH (2nd floor) by
1:00 pm on the day it is due
.
Question 1: (
15 marks
)
A random sample of 500 registered voters in the City Waterloo is asked if they favor the use of oxygenated fuels yearround to
reduce airpollution. If more than 315 voters responded positively, we will conclude that at least 60% of the voters favor the use
of these fuels.
a)
Find the probability of Type I error if exactly 60% of the voters favor the use of these fuels.
b)
What is the Type II error probability
ߚ
if 75% of the voters favor this action?
Solution:
The problem statement implies that H
0
: p = 0.6, H
1
: p > 0.6 and defines an acceptance region as
.
p
315
500
063
and rejection
region as
.
p
a)
The probability of a type 1 error is
08535
.
0
)
37
.
1
(
1
37
.
1
500
)
4
.
0
(
6
.
0
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 Fall '10
 Almehdawe,Eman
 Standard Deviation, Null hypothesis, Statistical hypothesis testing, Type I and type II errors, mean hole diameter

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