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Practice Test 3 Statistics Name: Directions: Work on these sheets. Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. In a statistics course, a linear regression equation was computed to predict the final-exam score ˆ from the score on the first test. The equation was y = 10 + 0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam? (a) 85.5 (b) 90 (c) 95 (d) 95.5 (e) none of the above 2. Refer to the previous problem. On the final exam Carla scored 98. What is the value of her residual? (a) –2.5 (b) 0 (c) 2.5 (d) 98 (e) none of the above 3. A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). A least-squares line was fitted to the data. Here is the residual plot from this least-squares fit. What does the residual plot tell you about the linear model? (a) The evidence is inconclusive. (b) The residual plot confirms the linearity of the fuel economy data. (c) The residual plot does not confirm the linearity of the data. (d) The residual plot clearly contradicts the linearity of the data. (e) none of the above 4. All but one of the following statements contains a blunder. Which statement could be correct? (a) There is a correlation of 0.54 between the position a football player plays and his weight. (b) We found a correlation of r = –0.63 between gender and political party preference. (c) The correlation between the gas mileage of a car and its weight is r = 0.71 mpg. (d) We found a high correlation (r = 1.09) between the height and age of children. (e) The correlation between planting rate and yield of tomatoes was found to be r = 0.23. 5. You have data for many families on the parents’ income and the years of education their eldest child completes. When you make a scatterplot, (a) the explanatory variable is parents’ income, and you expect to see a negative association. (b) the explanatory variable is parents’ income, and you expect to see a positive association. (c) the explanatory variable is parents’ income, and you expect to see very little association. (d) the explanatory variable is years of education, and you expect to see a negative association. (e) the explanatory variable is years of education, and you expect to see a positive association. Chapter 3 1 Test 3A 6. There is an approximate linear relationship between the height of females and their age (from 5 to 18 years) described by height = 50.3 + 6.01(age) where height is measured in centimeters and age in years. Which of the following is not correct? (a) The estimated slope is 6.01, which implies that children increase by about 6 cm for each year they grow older. (b) The estimated height of a child who is 10 years old is about 110 cm. (c) The estimated intercept is 50.3 cm, which implies that children reach this height when they are 50.3/6.01 = 8.4 years old. (d) The average height of children when they are 5 years old is about 50% of the average height when they are 18 years old. (e) My niece is about 8 years old and is about 115 cm tall. She is taller than average. 7. An AP Statistics student designs an experiment to see whether today’s high school students are becoming too calculator dependent. She prepares two quizzes, both of which contain 40 questions that are best done using paper-and-pencil methods. A random sample of 30 students participates in the experiment. Each student takes both quizzes—one with a calculator and one without. To analyze the data, the student constructs a scatterplot that displays the number of correct answers with and without a calculator for each of the 30 students. A least-squares regression yields the equation Calculator = 1.2 + 0.865(Pencil) r = 0.79 Which of the following statements is/are true? I. If the student had used Calculator as the explanatory variable, the correlation coefficient would remain the same. II. If the student had used Calculator as the explanatory variable, the slope of the least-squares line would remain the same. III. The standard deviation of the number of correct answers on the paper-and-pencil quizzes was larger than the standard deviation on the calculator quizzes. (a) I only (b) II only (c) III only (d) I and II only (e) I and III only 8. Scientists examined the activity level of a large number of fish at 7 different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are given below. What was the approximate actual activity level rating for the fish at a temperature of 20.4 C ? (a) 86 (b) 83 (c) 80 (d) 66 (e) 3 Chapter 3 2 Test 3A Part 2: Free Response Answer completely, but be concise. Show your thought process clearly. Questions 9–12 relate to the following. Joey read in his biology book that fish activity increases with water temperature, and he decided to investigate this issue by conducting an experiment. On nine successive days, he measures fish activity and water temperature (in degrees Fahrenheit) in his aquarium. Larger values of his measure of fish activity denote more activity. The figure below presents the scatterplot of his data. o o 450 o o o Activity o o 300 o o 69.0 72.0 75.0 78.0 81.0 H2Otemp 9. How would you describe the direction, form, and strength of the relationship from the scatterplot? 10. One of the following numbers is the correlation coefficient between fish activity and water temperature; circle the correct number: –0.20 0.03 0.52 0.86 11. If temperature were measured in degrees Celsius instead of degrees Fahrenheit, how would the 9 correlation change? Note that F C 32 . 5 12. Suppose a new point at (66, 500), that is, water temperature = 66F and fish activity = 500, is added to the plot. What effect, if any, will this new point have on the correlation between fish activity and water temperature? Justify your answer. Chapter 3 3 Test 3A Questions 13–17 relate to the following. At summer camp, one of Carla’s counselors told her that you can determine air temperature from the number of cricket chirps. 13. What is the explanatory variable, and what is the response variable? (Note: This is in the context of this problem, not in the biological sense.) EXPLANATORY: RESPONSE: To determine a formula, Carla collected data on temperature and number of chirps per minute on 12 occasions. She entered the data into her calculator and did 2-Var Stats. Here are some results: x = 166.8 s x = 31.0 y = 78.83 s y = 9.11 r = 0.461 14. Use this information to find the equation of the least-squares regression line. Show your work. 15. One of Carla’s data points was recorded on a particularly hot day (93F). She counted 249 cricket chirps in one minute. What is the residual for this data point? Show your method. 16. Interpret the value of r 2 in the context of this problem. 17. Suppose that Carla counted 249 chirps on a day when the temperature was 55F. If this point were the 13th data point, what effect, if any, would this 13th point have on (a) the slope and (b) the y intercept of Carla’s regression line? Explain. I pledge that I have neither given nor received aid on this test. _______________________________ Chapter 3 4 Test 3A