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The document includes the AP Statistics formula sheet covering descriptive, probability, and inferential statistics, plus key constants such as mean, variance, standard deviation, correlation, regression, confidence intervals, and hypothesis-testing forms. 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Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association is made up of more than 5,900 of the world’s leading educational institutions and is dedicated to promoting excellence and equity in education. Each year, the College Board helps more than seven million students prepare for a successful transition to college through programs and services in college readiness and college success—including the SAT® and the Advanced  \nPlacement Program®. The organization also serves the education community through research and advocacy on behalf of students, educators, and schools.  \n© 2012 The College Board. College Board, Advanced Placement Program, AP, AP Central, SAT, and the acorn logo are registered trademarks ofthe College Board. Admitted Class Evaluation Service and inspiring minds are trademarks owned by the College Board. All other products and services may be trademarks oftheir respective owners. Visit the College Board on the Web:  \n[www.collegeboard.org. Permission to use](www.collegeboard.org. Permission to use) copyrighted College Board materials may be requested online at:  \n[www.collegeboard.org/inquiry/cbpermit.html](www.collegeboard.org/inquiry/cbpermit.html).  \n[Visit the College Board on the Web: www.collegeboard.org](Visit the College Board on the Web: www.collegeboard.org).  \nAP Central is [the official online home for the AP Program: apcentral.collegeboard.org](the official online home for the AP Program: apcentral.collegeboard.org).  \n2012 AP® STATISTICS FREE-RESPONSE QUESTIONS  \nFormulas begin on page 3.  \nQuestions begin on page 6.  \nTables begin on page 14.  \n2012 AP® STATISTICS FREE-RESPONSE QUESTIONS  \nFormulas  \n(I) Descriptive Statistics ~~x~~ = Âx~~ni~~  \nsx =  n-1 1  (xi-x )2  \nsp =  \nˆy = b0 + b1x  \nb1 = Â~~ ~~(x~~i ~~-~~x  ~~)~~ ~~(y~~i ~~2-y~~  ~~) (xi -x )  \nb0 = y-b1x  \nr = ~~n~~-1~~ 1~~  ÊËÁ xis-x x ˆ¯˜ ÊËÁ is-y ˆ¯˜  \nb1  \n= r  sy   \nsx  \nsb =  \n1  \n2012 AP® STATISTICS FREE-RESPONSE QUESTIONS  \n(II) Probability  \nP (A » B) = P (A) + P(B) -P(A « B)  \nP (A B) = P~~ ~~(AP~~(~~«B~~)~~B)  \nE (X ) = μ x = Âxipi  \nVar(X) = s 2 =  (x- μ )2 p  \nx i x i  \nIf X has a binomial distribution with parameters n and p , then: P (X = k) = ÊÁËnkˆ¯˜ pk (1-p)n-k  \nμ x = np  \nsx = np(1-p)  \nμˆp  \nsˆp  \n= p  \nIf ~~x~~ is the mean of a random sample of size n from an infinite population with mean μ and standard deviation s, then:  \nμ ~~x~~ = μ  \nss~~x~~ =  n  \n2012 AP® STATISTICS FREE-RESPONSE QUESTIONS  \n(III) Inferential Statistics  \nStandardized test statistic: ~~stan~~statist~~d~~a~~rd d~~~~i~~-para~~ti~~o~~n~~amo~~f~~est~~t~~ear~~tistic~~  \nConfidence interval: statistic ± (critical value) ∑ (standard deviation of statistic)  \nSingle-Sample  \n\n| Statistic | Standard Deviation\u003Cbr>of Statistic |\n| --- | --- |\n| Sample Mean | s\u003Cbr> n |\n| Sample Proportion | \u003Cbr>p(1-p) n |\n\nTwo-Sample  \n\n| Statistic | Standard Deviation\u003Cbr>of Statistic |  |\n| --- | --- | --- |\n| Difference of\u003Cbr>sample means | \u003Cbr>Special case when s1 = s2 |  |\n|  | s | |\n| Difference of sample proportions | \u003Cbr>Special case when p1 = p2  p (1-p ) 1n1~~ ~~ ~~ ~~1n~~ ~~2~~ ~~\u003Cbr>|  |\n\nChi-square test statistic =  ~~ ~~(observede~~x~~p-eec~~t~~p~~d~~ected)2~~ ~~  \n2012 AP® STATISTICS FREE-RESPONSE QUESTIONS  \nSTATISTICS  \nSECTION II  \nPart A  \nQuestions 1-5  \nSpend about 65 minutes on this part of the exam.  \nPercent of Section II score—75  \nDirections: 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.  \n1. The scatterplot below displays the price in dollars and quality rating for 14 different sewing machines.  \n(a) Describe the nature of the associatio","cbCaibpu2LMcJose","https://ap.wps.com/l/cbCaibpu2LMcJose","pdf",371375,17,"English","# Section II\n## Part A\n## Questions 1-5","[{\"question\":\"What does Section II Part A require for scoring?\",\"answer\":\"You must show all your work and clearly indicate the methods used, since scoring is based on both the correctness of the methods and the accuracy and completeness of results and explanations.\"},{\"question\":\"What topics are covered in the included statistics formulas?\",\"answer\":\"The formulas cover descriptive statistics (including correlation and regression), probability rules and expected value/variance, and inferential statistics such as standardized test statistics and confidence intervals.\"},{\"question\":\"What is Question 1 about?\",\"answer\":\"It analyzes a scatterplot showing price and quality rating for 14 sewing machines, including describing association, identifying an influential machine for linear regression, and selecting machines based on higher quality and lower price criteria.\"}]","2012 AP® Statistics Free-Response Questions | PDF",1789902053,43]