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2019AP StatisticsFree-Response Questions 2019 The College Board. College Board, Advanced Placement, AP, AP Central, and the acorn logo areregistered trademarks of the College Board. Visit the College Board on the web: collegeboard.org.AP Central is the official online home for the AP Program: apcentraLcollegeboard.org.AP'0 CollegeBoard

2019 AP STATISTICS FREE-RESPONSE QUESTIONSFormulas begin on page 3.Questions begin on page 6.Tables begin on page 14.-2-

2019 AP STATISTICS FREE-RESPONSE QUESTIONSFormulasDescriptive Statistics(I)1 E (x — ,7)2,i1sx \Spk 1)4. (n2 1)4(n1 — I) (n2 — I)9 b0 b1 xb 1bor E(xi —— Y) y1 1 ( xi — x )(Yi — Y )ssxn —1Yilx(Y1— s,i)2n—2Sb 1111 (X i — )12

2019 AP STATISTICS FREE-RESPONSE QUESTIONS(II)ProbabilityP(A u B) P(A) P(B) — P(A n B)P(AlB) E(X) P(An B)P(B) Exi piVar(X) ax2—2) piIf X has a binomial distribution with parameters n and p, then:P(X k) (n)pk (1— p)"k1-tx flPIf is the mean of a random sample of size n from an infinitepopulation with mean p. and standard deviation a, then:aa—x —

2019 AP STATISTICS FREE-RESPONSE QUESTIONS(III)Inferential StatisticsStandardized test statistic:statistic —parameterstandard deviation of statisticConfidence interval: statistic (critical value) (standard deviation of statistic)Single-SampleStandard Deviationof StatisticStatisticaSample Mean1P(1 — 13)1Sample ProportionTwo-SampleStindara DeviationStatistic1 ",,2Difference ofsample means1 nicr22122Special case when al cr211a — —\n1 n2Difference ofsample proportionsiPi (1 — Pi. ) P2 (1 — P2)n2nilSpecial case when PI P2\ 11liP (1 — /3 )Chi-square test statistic (observed — expected)2expected

2019 AP STATISTICS FREE-RESPONSE QUESTIONSSTATISTICSSECTION IIPart AQuestions 1-5Spend about 1 hour and 5 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. The sizes, in square feet, of the 20 rooms in a student residence hall at a certain university are summarized in thefollowing histogram.250300150200Room Size (square feet)350(a) Based on the histogram, write a few sentences describing the distribution of room size in the residence hall.(b) Summary statistics for the sizes are given in the following .12134174253.5292315 2019 The College Board.Visit the College Board on the web: collegeboard.org.GO ON TO THE NEXT PAGE.-6-

2019 AP STATISTICS FREE-RESPONSE QUESTIONSDetermine whether there are potential outliers in the data. Then use the following grid to sketch a boxplot ofroom size.r1II1.11I--I1-J1JL-1Lr Ir-Ir1IIIII111r.7ITr 0160180240260220200(squarefeet)Room Size280300320340360(c) What characteristic of the shape of the distribution of room size is apparent from the histogram but not fromthe boxplot?2019 The College Board.Visit the College Board on the web: collegeboard.org.GO ON TO THE NEXT PAGE.-7-

2019 AP STATISTICS FREE-RESPONSE QUESTIONS2. Researchers are investigating the effectiveness of using a fungus to control the spread of an insect that destroystrees. The researchers will create four different concentrations of fungus mixtures: 0 milliliters per liter (ml/L),1.25 ml/L, 2.5 ml/L, and 3.75 ml/L. An equal number of the insects will be placed into 20 individual containers.The group of insects in each container will be sprayed with one of the four mixtures, and the researchers willrecord the number of insects that are still alive in each container one week after spraying.(a) Identify the treatments, experimental units, and response variable of the experiment.Treatments:Experimental units:Response variable:(b) Does the experiment have a control group? Explain your answer.(c) Describe how the treatments can be randomly assigned to the experimental units so that each treatmenthas the same number of units. 2019 The College Board.Visit the College Board on the web: collegeboard.org.GO ON TO THE NEXT PAGE.-8-

2019 AP STATISTICS FREE-RESPONSE QUESTIONS3. A medical researcher surveyed a large group of men and women about whether they take medicine as prescribed.The responses were categorized as never, sometimes, or always. The relative frequency of each category isshown in the 21200.32800.5400(a) One person from those surveyed will be selected at random.(i) What is the probability that the person selected will be someone whose response is never and who is awoman?(ii) What is the probability that the person selected will be someone whose response is never or who is awoman?(iii) What is the probability that the person selected will be someone whose response is never given that theperson is a woman?(b) For the people surveyed, are the events of being a person whose response is never and being a womanindependent? Justify your answer.(c) Assume that, in a large population, the probability that a person will always take medicine as prescribedis 0.54. If 5 people are selected at random from the population, what is the probability that at least 4 ofthe people selected will always take medicine as prescribed? Support your answer. 2019 The College Board.Visit the College Board on the web: collegeboard.org.GO ON TO THE NEXT PAGE.-9-

2019 AP STATISTICS FREE-RESPONSE QUESTIONS4. Tumbleweed, commonly found in the western United States, is the dried structure of certain plants that areblown by the wind. Kochia, a type of plant that turns into tumbleweed at the end of the summer, is a problem forfarmers because it takes nutrients away from soil that would otherwise go to more beneficial plants. Scientistsare concerned that kochia plants are becoming resistant to the most commonly used herbicide, glyphosate. In2014, 19.7 percent of 61 randomly selected kochia plants were resistant to glyphosate. In 2017, 38.5 percent of52 randomly selected kochia plants were resistant to glyphosate. Do the data provide convincing statisticalevidence, at the level of a 0.05, that there has been an increase in the proportion of all kochia plants that areresistant to glyphosate? 2019 The College Board.Visit the College Board on the web: collegeboard.org.GO ON TO THE NEXT PAGE.-10-

2019 AP STATISTICS FREE-RESPONSE QUESTIONS5. A company that manufactures smartphones developed a new battery that has a longer life span than that of atraditional battery. From the date of purchase of a smartphone, the distribution of the life span of the new batteryis approximately normal with mean 30 months and standard deviation 8 months. For the price of 50, thecompany offers a two-year warranty on the new battery for customers who purchase a smartphone. The warrantyguarantees that the smartphone will be replaced at no cost to the customer if the battery no longer works within24 months from the date of purchase.(a) In how many months from the date of purchase is it expected that 25 percent of the batteries will no longerwork? Justify your answer.(b) Suppose one customer who purchases the warranty is selected at random. What is the probability that thecustomer selected will require a replacement within 24 months from the date of purchase because the batteryno longer works?(c) The company has a gain of 50 for each customer who purchases a warranty but does not requirea replacement. The company has a loss (negative gain) of 150 for each customer who purchases a warrantyand does require a replacement. What is the expected value of the gain for the company for each [email protected] 2019 The College Board.Visit the College Board on the web: collegeboard.org.GO ON TO THE NEXT PAGE.-11-

2019 AP STATISTICS FREE-RESPONSE QUESTIONSSTATISTICSSECTION IIPart BQuestion 6Spend about 25 minutes on this part of the exam.Percent of Section II score-25Directions: 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.6. Emma is moving to a large city and is investigating typical monthly rental prices of available one-bedroomapartments. She obtained a random sample of rental prices for 50 one-bedroom apartments taken from a Website where people voluntarily list available apartments.(a) Describe the population for which it is appropriate for Emma to generalize the results from her sample.The distribution of the 50 rental prices of the available apartments is shown in the following histogram.109876zg, 5e 43210 L.1IE 1,600 2,000 2,400 2,800 3,200 3,600 4,000 4,400 4,800 5,200Rental Price(b) Emma wants to estimate the typical rental price of a one-bedroom apartment in the city. Based on thedistribution shown, what is a disadvantage of using the mean rather than the median as an estimate of thetypical rental price?(c) Instead of using the sample median as the point estimate for the population median, Emma wants to use aninterval estimate. However, computing an interval estimate requires knowing the sampling distributionof the sample median for samples of size 50. Emma has one point, her sample median, in that samplingdistribution. Using information about rental prices that are available on the Web site, describe how someonecould develop a theoretical sampling distribution of the sample median for samples of size 50.Because Emma does not have the resources to develop the theoretical sampling distribution, she estimates thesampling distribution of the sample median using a process called bootstrapping. In the bootstrapping process,a computer program performs the following steps. Take a random sample, with replacement, of size 50 from the original sample. Calculate and record the median of the sample. Repeat the process to obtain a total of 15,000 medians. 2019 The College Board.Visit the College Board on the web: collegeboard.org.GO ON TO THE NEXT PAGE.-12-

2019 AP STATISTICS FREE-RESPONSE QUESTIONSEmma ran the bootstrap process, and the following frequency table is the bootstrap distribution showing herresults of generating 15,000 medians.Bootstrap Distribution of 2,7952783,00022,5501,6732,812.5163,062.53The bootstrap distribution provides an approximation of the sampling distribution of the sample median.A confidence interval for the median can be constructed using a percentage of the values in the middle of thebootstrap distribution.(d) Use the frequency table to find the following.(i) Value of the 5th percentile:(ii) Value of the 95th percentile:(e) Find the percentage of bootstrap medians in the table that are equal to or between the values found inpart (d).(f) Use your values from parts (d) and (e) to construct and interpret a confidence interval for the medianrental price.STOPEND OF EXAM 2019 The College Board.Visit the College Board on the web: collegeboard.org.-13-

2019 AP STATISTICS FREE-RESPONSE QUESTIONSProbabilityTable entry for z is theprobability lying below z.Table A Standard normal 451,2776.3121.3483.3859.4247.4641

2019 AP STATISTICS FREE-RESPONSE QUESTIONSProbabilityTable entry for z is theprobability lying below z.Table A 0.7291.7611.7910.8186.8438.8

2019 AP STATISTICS FREE-RESPONSE QUESTIONS STATISTICS SECTION II Part B Question 6 Spend about 25 minutes on this part of the exam. Percent of Section II score-25 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. 6. Emma is