2 0 1 0 AP STATISTICS F R E E - R E S P O N S E QUESTIONS ( F o r m B)STATISTICSSECTION IIPart AQuestions 1-5Spend about 65 minutes on this part of the exam.Percent of Section II score—75Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on thecorrectness 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, andRiver Z—had become contaminated with pesticides because they were located near abandoned pesticide dumpsites. Measurements of the concentration of aldrin (a commonly used pesticide) were taken at twenty randomlyselected 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 Z345678Concentrations of Aldrin (ppm)9(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.3.4 4.0 5.6 3.7 8.0 5.5 5.3 4.2 4.3 7.38.6 5.1 8.7 4.6 7.5 5.3 8.2 4.7 4.8 4.6Construct 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 thestemplot but cannot be seen in the boxplot. 2010 The College Board.Visit the College Board on the Web: www.colIegeboard.com.GO ON TO THE NEXT PAGE.-6-
2004 AP STATISTICS FREE-RESPONSE QUESTIONS (Form B)STATISTICSSECTION IIPart AQuestions 1-5Spend about 65 minutes on this part of the exam.Percent of Section II grade—75Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on thecorrectness 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 heavybombardment of small celestial bodies. Scientists studied 11 impact craters on the Moon to determine whetherthere was any relationship between the age of the craters (based on radioactive dating of lunar rocks) and theimpact rate (as deduced from the density of the craters). The data are displayed in the scatterplot below.8.0()0 .7,0()06,(K)05,0004,0003,0002,0001,00000.4 »»« «0.91.4Age (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 usinglogarithms. The following computer output and residual plot were produced.Regression Equation: In(rate) 4.82 - 3.92 In(age)PredictorCoefSE 0.4514-8.690.000S 0.5977R-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 www.collegeboard.com/apstudents (for AP students and parents).GO ON TO THE NEXT PAGE.6
2004 AP STATISTICS FREE-RESPONSE QUESTIONS (Form B)4 a;18.104.22.168 6.5Filled Value7.58.5(b) Interpret the value of r .(c) Comment on the appropriateness of this linear regression for modeling the relationship between thetransformed variables.2. At a certain university, students who live in the dormitories eat at a common dining hall. Recently, somestudents have been complaining about the quality of the food served there. The dining hall manager decided todo a survey to estimate the proportion of students living in the dormitories who think that the quality of the foodshould be improved. One evening, the manager asked the first 100 students entering the dining hall to answer thefollowing question.Many students believe that the food served in the dining hall needs improvement. Do you think that thequality of food served here needs improvement, even though that would increase the cost of the meal plan?YesNoNo opinion(a) In this setting, explain how bias may have been introduced based on the way this convenience sample wasselected 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 andsuggest 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 inhopper cars. Filling equipment is used to load ore into the hopper cars. When functioning properly, the actualweights of ore loaded into each car by the filling equipment at the mine are approximately normally distributedwith a mean of 70 tons and a standard deviation of 0.9 ton. If the mean is greater than 70 tons, the loadingmechanism is overfilling.(a) If the filling equipment is functioning properly, what is the probability that the weight of the ore in arandomly 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 thatthe 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 www.collegeboard.coin/apstudents (for AP students and parents).GO ON TO THE NEXT PAGE.7
2 0 0 9 AP STATISTICS F R E E - R E S P O N S E Q U E S T I O N S ( F o r m B)STATISTICSSECTION IIPart AQuestions 1-5Spend about 65 minutes on this part of the exam.Percent of Section II score—75Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on thecorrectness 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 payon gasoline for their cars. In the United States, gasoline taxes are imposed by both the federal government andby 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—I0 5 10 15 20 25 30 35State Gasoline Taxes (in cents per gallon)(a) Based on the boxplot, what are the approximate values of the median and the interquartile range of thedistribution of state gasoline taxes, in cents per gallon? Mark and label the boxplot to indicate how youfound 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 ofcombined gasoline taxes. What are approximate values, in cents per gallon, of the median and interquartilerange of the new distribution of combined gasoline taxes? Justify your answer. 2009 The College Board. All rights reserved.Visit the College Board on the Web: www.collegeboard.com.-6-GO ON TO THE NEXT PAGE.
2008 AP" STATISTICS FREE-RESPONSE QUESTIONS (Form B)2. Four different statistics have been proposed as estimators of a population parameter. To investigate the behaviorof these estimators, 500 random samples are selected from a known population and each statistic is calculated foreach sample. The true value of the population parameter is 75. The graphs below show the distribution of valuesfor each statistic.Statistic A5075Statistic B100507575100Statistic DStatistic C50r-T5010075100(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. 2008 The College Board. All rights reserved.Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents).GO ON TO THE NEXT PAGE.-7-