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2009 Final

# 2009 Final - MATH 203 Final Examination Student Name...

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MATH 203 Final Examination April 27, 2009 Student Name: Student Number: McGill University Faculty of Science FINAL EXAMINATION MATH 203 Principles of Statistics I April 27th, 2009 9 a.m. - 12 Noon Answer directly on the test (use front and back if necessary). Calculators are allowed. One 8.5” × 11” two-sided sheet of notes is allowed. Language dictionaries are allowed. There are 17 pages to this exam and 2 pages of tables. The total number of marks for the exam is 100. Examiner: Professor Russell Steele Associate Examiner: Professor David Stephens 1

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MATH 203 Final Examination April 27, 2009 Question 1: (10 points) The Canadian government has decided that there was some suspicious, potentially illegal activity regarding a company’s revenue stream. As part of their investigation, they wanted to establish that there was a significant increase in the mean transaction amount before and after a particular event. The government statistician took a random sample of transactions with 50 customers who were billed both before and after the date of interest (i.e. each customer was billed twice). The data are summarized in the table below: Mean Std Dev 25%ile Median 75%ile Sample size Before event 98.82 20.49 83.99 101.2 109.3 50 After event 108.3 17.94 96.25 107.8 120.1 50 Difference [After - Before] 9.47 19.81 5.188 9.01 24.72 50 Test for a significant increase in the mean transaction amount before and after the event at α = 0 . 05. 2
MATH 203 Final Examination April 27, 2009 Question 2: (10 points) Professor Steele gave out a surprise quiz during one of his classes. The quiz had 3 questions. Each question was worth 2 points , however no partial credit was given. Assume that the probability distribution (i.e. probability mass function) for the number of correctly answered questions by a randomly selected student is: Number of correctly answered questions 0 1 2 3 Probability 0.05 0.20 0.40 0.35 (a) What is the distribution (i.e. the probability mass function) for the total score on the quiz for a randomly selected student? [2 points] (b) What is the expectation and variance of the total quiz score for a randomly selected student? [2 points] 3

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MATH 203 Final Examination April 27, 2009 (c) What is the distribution (i.e. the probability mass function) for the average (or mean ) of two randomly selected student quiz scores? [3 points] (d) What is the approximate distribution for the average (or mean ) of 100 randomly selected student quiz scores? [3 points] 4
MATH 203 Final Examination April 27, 2009 Question 3: (6 points) In a 1995 paper in Astrophysics and Space Science, Higgins and Henrikson discussed the distribution of gamma-ray bursts in halo neutron star-comet models. They based most of their conclusions on a simulation model where the velocities of comets ejected from globular cluster stellar systems were assumed to be Normally distributed with mean velocity (in km/s) equal to 200 and standard deviation 110.

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