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Unformatted text preview: Class Test 2 : Solution DATE: 2010 Instructor: Simin Seury Faculty of Liberal Arts & Professional Studies York University
AP/ECON 2500 3.0: Introductory Statistics for Economists I
Please note: the following only provides a brief guide. Your answer in exam is supposed to
include all steps (formula/calculation etc.) and explanation. Q1. The mailing list of a company that is planning to launch customer survey for one of their new
product that works as a diet supplement contains 60 percent non-smokers and 40 percent
smokers. The company calls 30 people chosen at random from the list.
(a) Calculate the probability of having 20 non-smoker out of the 30 people using Binomial
M has a binomial distribution with n = 30 and p = 0.6. 30 20
So P(M = 20) = (0.6) (0.4) = 0.1152. 20 (b) What is the probability that the first smoker is reached on the fourth call?
P(1st woman is the 4th call) = (0.6)3(0.4) = 0.0864
(c) Instead of reaching people from their mailing list, the company decides to do a door to door
survey in Toronto. It is known that Toronto, with a population of 2.48 million people, is a
multicultural city and the approximately 22% people in this city are born outside Canada.
The statistician hired for this job chooses an SRS of 1000 residents for a sample survey and
wants to find the probability that 250 or more of the people in this sample were born outside
Canada. Can s/he use the Normal approximation for the sampling distribution of a sample
proportion to answer this question? Justify your answer.
As a rule of thumb, the population of Toronto is much larger than 10 times the sample size n =
1000. So we can use the usual formula for the standard deviation of ˆ p. ...
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