AP® Statistics 2009 Free-Response Questions The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 5,600 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools and 3,800 colleges through major programs and services in college readiness, college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SAT®, the PSAT/NMSQT® and the Advanced Placement Program® (AP®). The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities and concerns. © 2009 The College Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, SAT, and the acorn logo are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. Permission to use copyrighted College Board materials may be requested online at: www.collegeboard.com/inquiry/cbpermit.html. Visit the College Board on the Web: www.collegeboard.com. AP Central is the official online home for the AP Program: apcentral.collegeboard.com. www.mymathscloud.com
2009 AP® STATISTICS FREE-RESPONSE QUESTIONS -4- (II) Probability ()()()()PA BPAPBPA B»= + - «()()()PA BPABPB«=()EXxpxii==Âμ()22Var( )xixXxpis== -ÂμIf X has a binomial distribution with parameters n and p, then: ()(1)nknkPX kppkʈÁ ̃Ë ̄-==-npx=μ(1)nppxs=-ˆpp=μ(1)ˆpppns-=If x is the mean of a random sample of size nfrom an infinite population with mean μ and standard deviation ,s then: x=μμxnss=www.mymathscloud.com
2009 AP® STATISTICS FREE-RESPONSE QUESTIONS -5- (III) Inferential Statistics standard deviation of statisticstatistic parameterStandardized test statistic:-()()Confidence interval: statistic critical valuestandard deviation of statistic∑±Single-Sample Statistic Standard Deviation of Statistic Sample Mean nsSample Proportion (1)ppn-Two-Sample Statistic Standard Deviation of Statistic Difference of sample means 221212nnss+Special case when 12ss=1211nns+Difference of sample proportions 112 212(1)(1)ppp pnn--+Special case when 12pp=()1pp-1211nn+()2observedexpectedChi-square test statisticexpected-=Âwww.mymathscloud.com
2009 AP® STATISTICS FREE-RESPONSE QUESTIONS © 2009 The College Board. All rights reserved. Visit the College Board on the Web: www.collegeboard.com. GO ON TO THE NEXT PAGE. -6- STATISTICS SECTION II Part A Questions 1-5 Spend about 65 minutes on this part of the exam. 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. A simple random sample of 100 high school seniors was selected from a large school district. The gender of each student was recorded, and each student was asked the following questions. 1. Have you ever had a part-time job? 2. If you answered yes to the previous question, was your part-time job in the summer only? The responses are summarized in the table below. Gender Job Experience Male Female Total Never had a part-time job 21 31 52 Had a part-time job during summer only 15 13 28 Had a part-time job but not only during summer 12 8 20 Total 48 52 100 (a) On the grid below, construct a graphical display that represents the association between gender and job experience for the students in the sample. www.mymathscloud.com
