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STATISTICS SECTION I Time – 45 minutes Number of Questions – 20 Percent of total grade – 50 Directions: Solve each of the following problems, using the available space for the scratchwork. Decide which is the best of the choices given and fill in the corresponding oval on the answer sheet. No credit will be given for anything written on the exam. Do not spend too much time on any one problem. 1. Following are the SAT math scores for an AP Statistics class of 20 students: 664, 658, 610, 670, 640, 643, 675, 650, 676, 575, 660, 661, 520, 667, 668, 635, 671, 673, 645, and 650. The distribution of scores is A. symmetric. B. skewed to the left. C. skewed to the right. D. uniform. E. bell-shaped. 2. Following is the stem plot of a data set of size 125 1 8 2 0013567789 3 0112333445666678899 4 000111222333445667788 5 000022233334444555666777778888899999999999 6 0001112223445566778899 7 01256679 8 12 What is the middle (median) of this set? A. 53 B. 54 C. 62 D. 63 E. 64 3. Suppose the average score on a national test is 500 with a standard deviation of 100. If each score is increased by 10%, what are the new mean and standard deviation? A. 500, 100 B. 550, 110 C. 550, 100 D. 500, 110 E. 550, 90 GO ON TO THE NEXT PAGE 4. In a certain southwestern city, the air pollution index averages 62.5 during the year with a standard deviation of 18.0. Assuming that the empirical rule is appropriate, the index falls within what interval 95% of the time? A. (8.5, 116.5) B. (26.5, 98.5) C. (44.5, 80.5) D. (45.4, 79.6) E. There is insufficient information to answer this question. 5. The following graph shows cumulative proportions with regard to outstanding balances on credit cards. 1 0.9 Cummulative Proportions 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 500 1000 1500 2000 2500 3000 3500 4000 Credit Card Outstanding Balances What is the interquartile range? A. $200 B. $600 C. $1550 D. $1750 E. $2000 6. Consider the following back-to-back stem plot: 73 2 642 3 37 7 4 246 9300 5 7 9920 6 0039 943 7 0299 8 8 349 9 8 Which of the following are true statements? I. The distributions have the same mean. II. The distributions have the same range. III. The distributions have the same variance. A. II only B. I and II C. I and III D. II and III E. I, II and III GO ON TO THE NEXT PAGE 7. Suppose a data set has a linear regression line of ŷ = 6 0.8x. if x = 5, what is y ? A. 2 B. 5 C. 10 D. 6 E. 5 8. You have the regression equation, ŷ = 2.4 0.2x, for the effect of streetlights per block (x), on crimes per month (y). The residual for a block with 10 streetlights and 1 crime a month is A. 0.6 B. 0.6 C. 0.4 D. 0.4 E. 12 9. The regression equation ŷ = 1278.5 0.5x shows the relationship between the number of calories consumed in a day (x) and marathon times in minutes (y) in a sample of world-class distance runners. Interpret the meaning of the slope in the equation stated above. A. A one-calorie increase in consumption per day results in a predicted increase of 0.5 minutes in marathon time. B. A one-calorie increase in consumption per day results in a predicted decrease of 0.5 minutes in marathon time. C. An increase of 0.5 calorie per day results in a predicted one-minute decrease in marathon times. D. A decrease of 0.5 calories leads to a predicted 1278.5 minutes increase in marathon times. E. None of the above. 10. In which of the following scenarios would it be most acceptable to do an interpolation using a least squares regression line? A. There is a high positive correlation. B. Residuals follow a linear pattern. C. There is a strong negative correlation, and the residuals follow a U-shaped pattern. D. There is a strong negative correlation, and the residuals are randomly scattered around the line y ŷ = 0. E. There is no correlation, and residuals are randomly scattered around the line y ŷ = 0. 11. If the association between two variables is exponential, which of the following is the general form of the regression equation for the logarithmic transformed data? A. ŷ = a + b log x B. ŷ = a + log xb C. log ŷ = a + bx D. ŷ = log a + log (bx) E. ŷ = log (ab) x GO ON TO THE NEXT PAGE 12. A scattered plot is suspected to be a power regression. After performing the logarithmic transformation of (log y, log x), a linear regression equation of Y = 0.2 + 0.4X is the result. When x = 2, the predicted value of ŷ is A. 2.0913 B. 0.32041 C. 1.0000 D. 10.0000 E. 0.1000 Use the following information to answer the next two questions. Some researchers were interested in whether the number of crimes committed during the summer is related to the outdoor temperature. The results of a survey of 150 municipal police departments revealed the following: Crime Rate Temperature Below Normal Above Below 12 8 5 Normal 35 41 24 Above 4 7 14 13. The distribution of temperature by above average crime rate is A. 0.08, 0.13, 0.33 B. 0.17, 0.67, 0.17 C. 0.14, 0.73, 0.13 D. 0.12, 0.56, 0.33 E. 0.24, 0.69, 0.08 14. Which of the following are correct interpretations of the two-way table? I. For police departments where the temperature is above average, the crime rate is most likely to be above average. II. For police departments where the crime rate is normal, the temperature is most likely to be normal. III. For police departments where the crime rate is above average, the temperature is most likely to be above average. A. I only B. II only C. III only D. I and II only E. II and III only ___________________________________________ GO ON TO THE NEXT PAGE Use the following information to answer the next two questions. The following tables show hypothetical data for two experimental treatments (Treatment A, Treatment B and their aggregated data) against two stages of cancer (Early and Advanced). “Remission” indicates a successful treatment. “Rate” is the proportion of remissions. Early Stage Advanced Stage Remissions Death Rate Remissions Death Rate A 5 1 0.833 A 4 6 0.400 B 10 4 0.714 B 1 4 0.200 Remissions Death Rate A 9 7 0.563 B 11 8 0.579 15. Which of the following demonstrates the Simpson’s Paradox? A. Both Treatment A and Treatment B have good success rate. B. When success rates for early and advanced cancers are kept separate, Treatment A has a higher success rate. But when data for the two stages are combined, Treatment B has a higher rate. C. When success rates for the two stages of cancers are kept together, Treatment A has a higher success rate for each stage of cancer, But when the two stages of cancer are separated, Treatment B has a higher success rate. D. Treatment A has a higher success rate no matter how the data are combined. E. Treatment B has a higher success rate no matter how the data are combined. 16. What is the lurking variable when the data for early and advanced cancers are combined? A. Treatment method (A or B) B. Number of treatments C. Stage of cancer (early or advanced) D. Quality of treatment (good or poor) E. Quality of hospital (good or poor) 17. The equation that would provide the best fit for the data (0,0) (4,40) (8, 64) (12,72) (16, 64) (20,40) (24,0) would be: A. ŷ= 40 + 0x B. ŷ= 40x C. ŷ= -0.5x + 12 D. ŷ= 40x + 12 E. ŷ= -0.5x2 + 12 18. Suppose there is a correlation of r=0.9 between parent SAT score and son/daughter SAT score. Which is the reasonable conclusion? A. 90% of the students with high scores had parents with high scores. B. 90% of students with parents had high scores C. 90% of the variation in student score can be explained by the parent score D. 10% of the deviation can be explained by the parent score E. 81% of the variation in student score can be explained by the parent score GO ON TO THE NEXT PAGE 19. If a collection of data that has been transformed (x, y ) has an LSRL: sqr ŷ= 11.2250 + .3742x. What would the predicted value (ŷ) if x = 35? A. 13.097 B. 24.322 C. 591.5597 D. 2.0989 x 1024 E. None of the above 20. If a collection of data that has been transformed (x, log y) has a LSRL: log ŷ= 1.8405 + 0.0067x What would the predicted value (ŷ) if x = 10? F. .067 G. 1.9075 H. 19.075 I. 80.8165 J. None of the above END OF SECTION I