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Test2_Spring05_06Solutions

Test2_Spring05_06Solutions - Engineering Statistics I Math...

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Engineering Statistics I; Math 223 Test 2, Spring 05-06 Name ___________________________________________________________ Instructions: You may use the following on this exam: front & back sides of two handwritten 6 x 4 note cards, a calculator, a blank Maple worksheet, the Maple help menu, a the Minitab worksheet that I am emailing to you, the Minitab help menu, and a blank Excel worksheet. I will provide you with a normal distribution table. There are 9 problems (with parts) on this exam. The point values of each problem are listed along with the problems. No partial credit will be given on the multiple choice questions. Since I will be giving partial credit on most problems, please show as much work as possible to earn points. Clearly indicate your final answers by circling them. If you use Maple, Minitab or Excel, state this and let me know what commands (Maple), operations (Minitab or Excel) you performed. Points will be deducted, even if you supply the correct answer , if you do not have convincing evidence to support your answer. Number of Points Page 1: 14 points Page 2: 17 points Page 3: 17 points Page 4: 20 points Page 5: 8 points Page 6: 16 points Page 7: 8 points Total: 100 points

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1 1. [+4, +3, +3, +4, +3, +3, +3, +4, +4] The population in Mexico for years 1980 through 1986 is given in the table below. Year 1980 1981 1982 1983 1984 1985 1986 Population (in millions) 67.38 69.13 70.93 72.77 74.66 76.6 78.59 (a) Calculate the value of the sample correlation coefficient r . If you compute it by-hand or in Maple, please sketch out the steps you performed; otherwise, indicate Minitab was used for the computation. r = 1 (b) Which of the following is the best interpretation of the sample correlation coefficient r ? Circle the correct response. (A) It tells us by what amount the proportion of the population increases as the year is increased. (B) It gives us an indication of the strength of linear relationship between year and population. (C) It gives us an indication of the strength of any type of relationship between year and population. (D) It tells us the amount of variation in the population data that can be explained by the year. (E) It is simply the sum of the squared residuals, 7 1 2 ˆ i i i y y , and tells us the amount of variation about the linear regression line. (c) How would the value of r be affected if the population were expressed in thousands instead of millions? (A) The value of r would be 1000 times its value computed in millions (B) The value of r would be 1/1000 of its value computed in millions (C) The value of r would be double its value computed in millions (D) The value of r would not change (E) The value of r would become r 2 (d) Determine the equation of the least squares regression line and report it below in terms of the predictor variable x and response variable y ˆ (i.e., y ˆ = …). If you use Maple, email me your worksheet for determining the least squares regression line; otherwise, indicate Minitab for the computation.
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