# 2006 - MATH 203 Final Examination December 7 2006 Student...

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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. 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) (b) What percentage of social workers’ offices are between 8.5 and 10.5 square meters? (2 points) (c) What percentage of social workers’ offices are exactly 9.0 square meters? (2 points) 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 test for fathers of very low birthweight babies. The second and third plots summarize the same data, only in histogram form, with the mothers at the top and the fathers at the bottom. Assume that the mothers and fathers are independently sampled, i.e. they are not paired. Mothers Fathers 40 50 60 70 80 Histogram of MSA Mothers’ Anxiety Scores Frequency 20 30 40 50 60 70 80 90 5 15 Histogram of FSA Fathers’ Anxiety Scores Frequency 20 30 40 50 60 70 80 90 5 15 4 MATH 203 Final Examination December 7, 2006 Here are the summary statistics for the two groups: Mean Variance 25%ile Median 75%ile Min Max Mothers 57.42 137.16 48.00 55.00 64.00 37.00 84.00 Fathers 52.16 128.81 45.00 50.00 59.00 34.00 80.00 (a) Construct a 90% confidence interval for a mother’s mean anxiety score for those mothers...
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2006 - MATH 203 Final Examination December 7 2006 Student...

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