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Unformatted text preview: STAT 21 Spring 2009 - Section 2, Practice questions and solutions Brief solutions can be found at the end. In the exam, you are expected to justify the reasoning for all answers. Work out all answers in decimals to at least two places. 1. A class has 4 sections. The following are some summary statistics of scores in 4 sections of a class. Section A B C D average midterm score 67 60 72 70 SD of midterm scores 14 17 14 13 average final score 62 61 80 72 SD of final scores 12 16 13 15 (a) A scatter diagram consists of 4 points. The co-ordinates of the points are (67, 62), (60, 61), (72, 80), and (70, 72). The correlation is 0.848. (You can check that by calculation if you want, but it is not necessary.) The correlation between the midterm scores and final scores of students in this class (i) is less than 0.848 (ii) is equal to 0.848 (iii) is more than 0.848 (b) The SD of the final scores of students in this class (i) is less than (ii) is equal to (iii) is more than the SD of the list 62, 61, 80, 72. 2. Midterm scores in a class have an average of 75 and an SD of 10. Final exam scores in that class have an average of 60 and an SD of 16. The correlation between midterm and final scores is 0.5 and the scatter diagram is football shaped. Students complain that the final was too hard so the instructor gives each student 15 more points on the final. (a) The correlation between the midterm scores and the new final exam scores is ————–. (b) The correlation between the old final exam scores and the new final exam scores is ——————. 3. The average height of a large group of children is 43 inches and the SD is 1.2 inches. The average weight of these children is 40 pounds and the SD is 2 pounds. A scatter diagram is drawn, with height on the horizontal axis and weight on the vertical axis. The scatter diagram is football shaped. The correlation between the two variables is 0.65. The regression line for estimating weight based on height is drawn through the scatter. (a) One of the children weighs 37 pounds and is 42 inches tall. The point corresponding to this student on the scatter diagram (pick one) (i) is above (ii) is on (iii) is below (iv) cannot be placed relative to the regression line for estimating weight based on height. (b) A child who is 43 inches tall is estimated to weigh ——– pounds, give or take ————– pounds. (c) A child who is 41.5 inches tall is estimated to weigh ———– pounds, give or take ————– pounds. (d) Of the children who are 41.5 inches tall, about what percent weigh more than 40 pounds? (e) Among all the children in the group, about what percent weigh more than 40 pounds? (f) About 80% of the children have weights that are within ——— pounds of the average....
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- Fall '08
- Mass, Statistical hypothesis testing, Simple random sample