2010 AP STATISTICS FREE-RESPONSE QUESTIONS (Form B)

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1 2010 AP FREE-RESPONSE QUESTIONS (Form B) Percent of Section II score 75 Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1. As a part of the United States Department of Agriculture's Super Dimip cleanup efforts in the early 1990s, various sites in the country were targeted for cleanup. Three of the targeted sites River X, River Y, and River Z had become contaminated with pesticides because they were located near abandoned pesticide dump sites. Measurements of the concentration of aldrin (a commonly used pesticide) were taken at twenty randomly selected locations in each river near the dump sites. The boxplots shown below display the five-number summaries for the concentrations, in parts per million (ppm) of aldrin, for the twenty locations that were sampled in each of the three rivers. River X- RivcrY - River Z Concentrations of Aldrin (ppm) (a) Compare the distributions of the concentration of aldrin among the three rivers. (b) The twenty concentrations of aldrin for River X are given below Construct a stemplot that displays the concentrations of aldrin for River X. (c) Describe a characteristic of the distribution of aldrin concentrations in River X that can be seen in the stemplot but cannot be seen in the boxplot The College Board. Visit the College Board on the Web: -6-

2 2004 AP FREE-RESPONSE QUESTIONS (Form B) Percent of Section II grade 75 Directions: Show all 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 explanation. 1. The Earth's Moon has many impact craters that were created when the inner solar system was subjected to heavy bombardment of small celestial bodies. Scientists studied 11 impact craters on the Moon to determine whether there was any relationship between the age of the craters (based on radioactive dating of lunar rocks) and the impact rate (as deduced from the density of the craters). The data are displayed in the scatterplot below. 8.0()0. 7,0()0-6,(K)0 5,000 4,000 3,000 2,000 1,000 0»»«« Age (in billions of years) (a) Describe the nature of the relationship between impact rate and age. Prior to fitting a linear regression model, the researchers transformed both impact rate and age by using logarithms. The following computer output and residual plot were produced. Regression Equation: In(rate) = In(age) Predictor Coef SE Coef T P Constant In(age) S = R-Sq = 89.4% R-Sq (adj) = 88.2% Copyright 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents). 6

3 2004 AP FREE-RESPONSE QUESTIONS (Form B) 4> a; Filled Value (b) Interpret the value of r. (c) Comment on the appropriateness of this linear regression for modeling the relationship between the transformed variables. 2. At a certain university, students who live in the dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food served there. The dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question. Many students believe that the food served in the dining hall needs improvement. Do you think that the quality of food served here needs improvement, even though that would increase the cost of the meal plan? Yes No No opinion (a) In this setting, explain how bias may have been introduced based on the way this convenience sample was selected and suggest how the sample could have been selected differently to avoid that bias. (b) In this setting, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been worded differently to avoid that bias. 3. Trains carry bauxite ore from a mine in Canada to an aluminum processing plant in northern New York state in hopper cars. Filling equipment is used to load ore into the hopper cars. When functioning properly, the actual weights of ore loaded into each car by the filling equipment at the mine are approximately normally distributed with a mean of 70 tons and a standard deviation of 0.9 ton. If the mean is greater than 70 tons, the loading mechanism is overfilling. (a) If the filling equipment is functioning properly, what is the probability that the weight of the ore in a randomly selected car will be 70.7 tons or more? Show your work. (b) Suppose that the weight of ore in a randomly selected car is 70.7 tons. Would that fact make you suspect that the loading mechanism is overfilling the cars? Justify your answer. Copyright 2004 by College Entrance Examination Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for AP students and parents). 7

4 2009 AP FREE-RESPONSE QUESTIONS (Form B) Percent of Section II score 75 Directions: Show all 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 and completeness of your results and explanations. 1. As gasoline prices have increased in recent years, many drivers have expressed concern about the taxes they pay on gasoline for their cars. In the United States, gasoline taxes are imposed by both the federal government and by individual states. The boxplot below shows the distribution of the state gasoline taxes, in cents per gallon, for all 50 states on January 1, I I I I I I I I I I I I I I I I I State Gasoline Taxes (in cents per gallon) (a) Based on the boxplot, what are the approximate values of the median and the interquartile range of the distribution of state gasoline taxes, in cents per gallon? Mark and label the boxplot to indicate how you found the approximated values. (b) The federal tax imposed on gasoline was 18.4 cents per gallon at the time the state taxes were in effect. The federal gasoline tax was added to the state gasoline tax for each state to create a new distribution of combined gasoline taxes. What are approximate values, in cents per gallon, of the median and interquartile range of the new distribution of combined gasoline taxes? Justify your answer The College Board. All rights reserved. Visit the College Board on the Web: -6-

5 2008 AP" FREE-RESPONSE QUESTIONS (Form B) 2. Four different statistics have been proposed as estimators of a population parameter. To investigate the behavior of these estimators, 500 random samples are selected from a known population and each statistic is calculated for each sample. The true value of the population parameter is 75. The graphs below show the distribution of values for each statistic. Statistic A Statistic B r-t Statistic C Statistic D (a) Which of the statistics appear to be unbiased estimators of the population parameter? How can you tell? (b) Which of statistics A or B would be a better estimator of the population parameter? Explain your choice. (c) Which of statistics C or D would be a better estimator of the population parameter? Explain your choice The College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and (for students and parents). -7-