final_2006

final_2006 - MATH 203 Final Examination December 7 2006...

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Unformatted text preview: MATH 203 Final Examination December 7, 2006 Student Name: Student Number: McGill University Faculty of Science FINAL EXAMINATION MATH 203 Principles of Statistics I December 7th, 2006 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 15 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 Keith Worsley 1 MATH 203 Final Examination December 7, 2006 Question 1: (8 points) The Mississippi Department of Transportation collected data on the number of cracks (called crack intensity) in an undivided two-lane highway using van-mounted state-of-the-art video technology (Journal of Infrastructure Systems, March 1995). The mean number of cracks found in a sample of eight 50-meter sections sections of the highway was ¯ x = 2 . 10 with a variance of s 2 = 0 . 011. Suppose the American Association of State Highway and Transportation Officials (AASHTO) recommends a maximum mean crack intesity of 1.0 for safety purposes. Test the hypothesis that the true mean crack intensity of the Mississippi highway exceeds the AASHTO recommended maximum. Use α = 0 . 10. State your assumptions. Answer: The hypotheses of interest for this question are: H : μ ≤ 1 . H A : μ > 1 . Therefore, we would calculate a test statistic of: Z = ¯ X- μ S/ √ n = 2 . 10- 1 . . 011 / 8 = 29 . 66 Because 29 . 66 > t . 1 , 7 = 1 . 41, we can clearly reject the null hypothesis and conclude that mean crack intensity exceeds the maximum with Type I error rate 0.10. For this test to be valid, we must assume that the numbers of cracks are randomly sampled and normally distributed. 2 MATH 203 Final Examination December 7, 2006 Question 2: (6 points) The amount of office space allocated to social workers in provincial agencies is an approximately normally distributed random variable with a mean of 9.0 square meters and a standard deviation of 0.6 square meters. (a) What percentage of social workers’ offices are larger than 10.5 square meters? (2 points) Pr ( Y > 10 . 5) = Pr ( Z > 10 . 5- 9 . . 6 ) = Pr ( Z > 2 . 5) = 0 . 0062 (b) What percentage of social workers’ offices are between 8.5 and 10.5 square meters? (2 points) Pr (8 . 5 < Y < 10 . 5) = Pr ( 8 . 5- 9 . . 6 < Z < 10 . 5- 9 . . 6 ) = Pr (- . 83 < Z < 2 . 5) = 0 . 7905 (c) What percentage of social workers’ offices are exactly 9.0 square meters? (2 points) Because the data are normally distributed, the probability of exactly 9.0 square meters is 0. 3 MATH 203 Final Examination December 7, 2006 Question 3: (10 points) The figure below shows two side-by-side boxplots. The one on the left is a boxplot of 45 anxiety test scores for mothers who have very low birthweight babies, where a higher score implies more anxiety. The one of the right is a boxplot of 45 anxiety scores from the same testimplies more anxiety....
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final_2006 - MATH 203 Final Examination December 7 2006...

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