MSci609_winter2011_Assignment_3_sol -...

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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 year-round to reduce air-pollution. 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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MSci609_winter2011_Assignment_3_sol -...

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