SECTION I Number of Questions 14 Percent of Total Grade 50

Transcription

1 AP Stats Chap 8-9 Practice Test Name Pd SECTION I Number of Questions 14 Percent of Total Grade 50 Directions: Solve each of the following problems, using the available space (or extra paper) for scratchwork. Decide which is the best of the choices given and place that letter on the ScanTron sheet. No credit will be given for anything written on these pages for this part of the test. Do not spend too much time on any one problem. 1. The scatterplot below displays world populations (in millions) for years Where the population is an estimate, the lower estimate is given. For what range of years is a linear model appropriate? A. A linear model should not be used for any part of the data. B. A linear model should be used for each pair of adjacent points. C. A single linear model is appropriate for the entire data set. D. One linear model is appropriate for the years 0 through 600 and another linear model for the years 600 through E. One linear model is appropriate for the years 0 through 1000 and another linear model for the years 1400 through 1800.

2 2. The table below shows the gestation (in days) and average longevity (in years) for a number of different mammals: Gestation (days) Average Longevity (years) Black Bear Domestic Cat Monkey Lion Horse Gorilla Gray Squirrel The scatterplot and line of best fit are shown here: The regression analysis of this data yields the following values: Variable Coefficient constant 9.90 gestation Use this information to predict the average longevity (to the nearest tenth of a year) of an African elephant whose gestation is 660 days. A years B years C years D years E years

3 3. The figure below examines the association between life expectancy and computer ownership for several countries. Also shown are the equation and R 2 value from a linear regression analysis of the data. What is the best conclusion to draw from the figure? A. Although the association is strong, computer ownership probably does not promote longevity. Instead, national per capital wealth is probably a lurking variable that drives both life expectancy and computer ownership. B. Clearly, there must be some as-yet unknown health benefit associated with using computers. C. Persons who live longer buy more computers over the course of their longer lifetimes. D. Exposure to the radiation from computer monitors is causing a clear decline in life expectancy. E. Computer ownership promotes health and long life, probably due to the greater access that computer owners have to health information on the Internet. 4. Which of the following scatterplots of residuals suggests that a linear model may not be applicable? I. II. III. IV. A. II B. I C. III D. IV E. none of these

4 5. If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope of the line of best, b, and to the correlation, r? A. both will decrease B. both will increase C. both will remain the same D. b will increase and r will decrease E. b will decrease and r will increase 6. One of the important factors determining a car s fuel efficiency is its weight. This relationship is examined for 11 cars, and the association is shown in the scatterplot below. If a linear model is considered, the regression analysis is: Dependent variable: Fuel Efficiency R-squared = 84.7% VARIABLE COEFFICIENT Intercept Weight What does the slope say about this relationship? A. Gas mileage decreases an average of mpg for each thousand pounds of weight. B. Gas mileage decreases an average of mpg for each thousand pounds of weight. C. Gas mileage decreases an average of mpg for each thousand pounds of weight. D. Gas mileage increases an average of mpg for each thousand pounds of weight. E. Gas mileage increases an average of mpg for each thousand pounds of weight.

5 7. The relationship between two quantities, X and Y, is examined and the association is shown in the scatterplot below. What re-expression of Y should be tried as a starting point? A. log( Y) against X B. 1 against X Y C. 2 Y against X D. 1 ( ) log Y against X E. Y against X 8. Consider the data listed in the following table: X Y Create an appropriate model. What re-expression of Y does this model involve? A. 2 y B. log y C. 1 y D. 1 E. y y

6 9. Consider the data listed in the following table: X Y Create an appropriate model. Estimate the value of Y when X = 33. Round your answer to four decimal places. A B C D E Dioxins are a class of long-lived and highly toxic pollutants. The topsoil concentration in parts per million (ppm) are shown in the table as a function of distance from the dump where they were collected. Distance from dump (meters) Dioxin concentration (ppm) Re-express the dioxin concentration levels. Then determine the regression equation and coefficient of determination for the re-expressed data. 2 2 dioxin = distance ; R = A. ( ) ( ) ( ) ( ) 2 B. log dioxin = distance ; R = C. 2 dioxin = ( distance ); R =

7 D. E. 1 2 = ( distance ); R = dioxin 1 2 = ( distance ); R = dioxin

8 11. A company s sales increase by the same amount each year. This growth is A. logarithmic B. quadratic C. power D. exponential E. linear 12. Another company s sales increase by the same percent each year. This growth is A. power B. linear C. exponential D. quadratic E. logarithmic 13. Which of the following is not a goal of re-expressing data? A. Make the spread of several groups more alike. B. Make the scatter in the scatterplot spread out evenly rather than following a fan shape. C. Make the form of a scatterplot more nearly linear. D. Make the distribution of a variable more symmetric. E. All of the above are goals of re-expressing data. 14. The model distance= ( speed) can be used to predict the stopping distance (in feet) for a car traveling at a specific speed (in mph). According to this model, about how much distance will a car going 65 mph need to stop? A feet B feet C. 4.3 feet D feet E feet

9 SECTION II Part A Questions Percent of Section II Grade 75 Directions: Show all of your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanations. Home-Game Attendance. The total home-game attendance for major-league baseball is the sum of all attendees for all stadiums during the entire season. The home attendance (in millions) for a number of years is shown in the table here. 15. Make a scatterplot showing the trend in home attendance. Year Home Attendance (millions) Describe what you see. 17. Determine the correlation and comment on its significance Find the equation of the line of regression. 18.

10 19. Interpret the slope of the equation in context. 20. Use your model to predict the home attendance for How much 20. confidence do you have in your prediction? Explain. 21. The actual home attendance in 1998 was 70.6 million. Calculate the residual for Label this as an underpredition or an overprediction. 21. residual - label - Adding a Point. For Questions 22-26, use the following scatterplot of eight original points. Questions Scatter Plot Draw a Line of Best Fit through these original eight points. 23. Add an additional point, L, that has high leverage but a small residual x 24. Add an additional point, I, that has high influence that might change the sign (positive/negative) of the slope of the original line. 25. Add an additional point, C, that is far away from the original eight points, but that is consistent with the pattern of the original line. 26. Add an additional point, M, with little-to-no residual that would do almost nothing to the slope and the y-intercept of the original line.

11 SECTION II Part B Question 27 Percent of Section II Grade 25 Directions: Show all of your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanations. Consumer Price Index. The consumer price index (CPI) is a measure of the relative cost of goods in the US for a particular year. The table here shows the CPI for various years beginning in Year CPI a. Use an appropriate re-expression of the data to develop a model that can be used for predicting CPI values. 27a. 27b. Use your model to predict the CPI for b. 27c. State which rung of the Ladder of Powers you used for your re-expression and explain why you chose this rung. 27c.

12 AP Stats Chap 9-10 Practice Test SOLUTIONS 1. E 2. D 3. A 4. A 5. E 6. C 7. A 8. B 9. A 10. D 11. E 12. C 13. E 14. A The data shows a strong, positive, linear relationship with the exception of one very strange outlier in 1981; the year of the lock-out which canceled almost 40% of the games that season. 17. r = The correlation is not very large even though the trend looks quite strong. The obvious outlier at year 1981 is exerting influence on the model equation. 18. attendance = ( year) 19. The slope of the line indicates that for every one year increase, the home attendance increases by about 1.52 million fans Only weak confidence should be placed in this prediction. First, the outlier at 1981 demonstrates that the actual data is subject to some unusual disturbances. Second, this outlier is exerting a large amount of influence on the model, pulling the line towards it. Third, 1998 is an extrapolation of 10 years past the last data point we have. 21. residual = 2.5 million, which is an underprediction

13 22. Questions Scatter Plot x Questions Scatter Plot 26 I M L C x 27a. log CPI = ( year) 27b c. I chose to stop on the log rung of the ladder since the scatterplot of the original data was exponential, the R 2 value for the log re-expression was the highest (0.980), the re-expressed scatterplot looks very linear, the re-expressed residual plot is somewhat scattered, and the next rung on the ladder is too far (the scatterplot starts to bend back in the opposite direction).