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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” twosided 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 twolane highway using vanmounted stateoftheart video technology (Journal of Infrastructure Systems, March 1995). The mean number of cracks found in a sample of eight 50meter 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 sidebyside 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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 Spring '08
 Dr.JoseCorrea
 Statistics, Standard Deviation, Null hypothesis

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