EASED EXAM ee ea ee AP Statistics CONTAINS: © Multiple-Choice Questions and Answer Key © Free-Response Questions, Scoring Guidelines, and Sample Student Responses and Commentary © Statistical Information About Student Performance on the 1997 Exam Advanced Placement Program”College Board Regional Offic National Office: Wade Cusry/Philip Arbotino/Charlone Gill/Erederick Wright 5 Columbus Avenue, New York, NY 10023-6992 (212) 713-8000 E-mail: weury al board org, parboline @collegeboard.org,cgill@collegeboard org, fsright@collegeboard.org Middle Sates: Mary Alice MeCutiough Suite 410, 3440 Marker Steet, Philadelphia, PA 19104-3338 (215) 387-7600 E-mail: mmecullough@collegeboard.org (Serving Delaware, District of Columbia, Maryland, New New York, Pennsylvania, and Puerto Rico) Midwestern: Bob MeDenowgh Paula Herron/Ann Winship Suite 1001, 1560 Sherman Avenue Evanston, IL 60201-4805 (847) 866-1700 E-mail: rmedonough@collegeboard.org, pherron @collegeboard.org awiuship@ collegeboard. org (Serving Iinois, Indiana, lows, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Dakota, Ohio, South Dakota, West Virginia, and Wisconsin) \Naw England: Fred Wetzel £30 Totten Pond Road, Waltham, MA 0245-1982 (781) 890-9150 E-mail: fwetzel@collegeboard org (Serving Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont) Souihern: Geottrey Freer/Tom New Suine 240, 100 Crescent Centre Parkway, Tucker. GA 30084-7039) (770) 908-9737 E-mail: gfreer@collegeboard org, tnew @collegeboard (Serving Alabama, Florida, Georgia, Kentucky, Louisiana, Mississippi, North Carolina, South Carolina, Tesnessee, snd Virginia) Southyvestent: Frances BrownvScott Kampmeiet/Joe Millict/Mondy Raibon Suite 1050, 98 San Jacinto Boulevard, Austin, TX 78701-4039 2) 72-0298 E-mail: forown @e Negeboard org, skampmeies@eall hoard.or, millet @collegeboard.or mraibon@collegeboard.org (Serving Arkansas, New Mexico, Oklahoma, and Texas) Dallas/Fi. Worth Memoplex AP Office: Kay Wil P.O, Box 19666, Room 108, 600 South West Street, Arlington, TX 76019 @171272-7200 E-mail: kwilson@collegeboaré.or3 Wester: Claire Pelton, Gail Chapman Suite 480, 2099 Gateway Place, San Jose, CA 95110-1017 (408) 452-1400 E-mail: cpelton@collegeboard.org, hapman@collegeboard.ong (Serving Alaska, Asienna, California, Colorado, Hawaii, Idaho, Montana, Nevada, Oregon, Utah, Washington, and Wyoming) AP Consultant in Canada: George Ewontis 212-1755 Springfield Road Kelowna, B.C., Canada VIY SVS {250} 861-9050; (800) 667-4548 in Canada only E-mail: gewonus@ap.ca- The Advanced Placement Examination _ in Statistics Contains: @ Maltiple-Choice Questions and Answer Key ® Free-Response Questions, Scoring Guidelines, and Sample Student Responses and Commentary ® Statistical Information about Student Performance on the 1997 Exam‘This booklet was palace y Elbetonl Testing Service (ETS), which deol and amines te examination ofthe Ruvanocd Paceent Program for ih Callge Bosr. Pension = herby gre 0 ay ‘pot sesnization or ntion to rprogue thi booklet He gua for eo st, WO fae ivi tht copyeh rene re enc lrpradcad eps xsl sx hey appear his Dokl. Ts peisson dos ot ppt ny thay eyed mato tht may in is ook “Te Colley: Bou an Edson Testing Service (ETS) fe deste othe pil of egel oppor, ‘nd tc eric nd engayman pls se aided oy tat pint Funded in 500, he College Bur ia serps eden soca al suport cae Peetion stl tention tiger sluestion fr stot uh wr tah the ono cella fs mene sates ners edi staal egnations inal atss the Bod ponte city ooh vier ge bitoni Teng at siesta acres rotor stadt a th tant tosaso incall werk. Tho Cale Bead ‘Ghnpion hy mans of spo acs curl development seanent fides, pene ad bao lon ofeorldevelpet foun poly alyssa pbc arch eden xc ol Sen Capit © 198 by Coles Ente Examination Bord and Fain Tsing Serie. Al igh ere College Board, Athaced Place Progra. AP. Coles plore. Cllege Best Online and he aon oes So reghteed wagon ft Cllege Eetrsns Examination Bost ‘THE COLLEGE BOARD: EDUCATIONAL EXCELLENCE FOR ALL, STUDENTS,Ci The AP Process | Who Develops the AP Statistics Exam? © How Do They Develop It? ® Section I # Section II = Question Types 1 Multiple Choice 1 Free Response Scoring che Exam Who Scores the AP Statistics Exam? = Ensuring Accuracy 1 How the Scoring Guidelines are Created w Training Faculty Consultants to Apply the Scoring Guidelines = Maintaining the Scoring Guidelines Preparing Students for the Exam | Teacher Support ‘This chapter will give you a brief overview of what goes on behind the scenes during the development and, grading of the AP Sratisties Exam. You can find more derailed information in the “Technical Corner” of the AD website (wwvzcollegeboard.org/ap) Who Develops the AP Statistics Exam? The AP Statistics Development Committee, working ‘wich content experts ac Educational Testing Service (ETS), is responsible for creating the exam. This committee is made up of eight teachers from secondary schools, colleges, and universities in different pacts of the United States. The members provide different perspectives: AP high school teachers offer valuable advice regarding realistic expectations when matters of content coverage, skills required, and clarity of phrasing are addressed. On the other hand, college and university faculty members ensure that the questions are at the appropriate level of difficulty for an introductory college course in statistics. Each member typically serves for three years, Another person who aids in the development process is the Chief Faculty Consultant (CEC). He or she attends every committee meeting to ensure that the free-response questions selected for the exam can be scored reliably. You can find out more about the role of the CFC, and the scoring process in general, on pages 2-4, How Do They Develop It? Ir cakes at lease two years to develop each AP Statistics Exam. The development process is different for multiple-choice and free-response sections: Section | 1, Each commitcee member independently writes a selection of multiple-choice questions based on the course content outline. 2. The committee convenes to review these draft questions, and eliminates any language, symbols, or content that may be offensive to major subgroups of the test-taking population. In addition, statistical procedures help the committee identify possibly unfair items. 3. Most of the multiple-choice questions are pretested in college classes to obtain some estimate of the question’ level of difficulty. B The questions that make it through these screening processes are assembled according to test specifica- tions developed by the committee and, after further editing and checking, comprise Section I of the AP Statistics Exam. ‘The committee controls the level of difficulty of the multiple-choice section by including a variety of questions at different levels of difficuley.Section Il 1. Individual committee members write a selection of free-response questions based on the course content outline, 2. The committee reviews and refines draft questions, and determines which will work well far the AP Exam. They consider, for example, whether the questions will offer an appropriate level of difficulty and whether they will elicit answers that allow faculty consultants to discriminate among the responses along @ particular scoring scale, An ideal question enables the stronger students to demon- strate their accomplishments while revealing the limitations of less advanced students. In the last stage of development, committee mem- bers give approval to a final draft of all mulciple-choice and ftee-response questions. This review takes place several months before the administration of che exam. Ques n Types ‘The AP Exam in Statistics contains a 90-minute multiple-choice section and a 90-minute fiee-response section. The two sections are designed to complement each other and to meet the overall course objectives and exam specificasions. Multiple-choice questions are obviously useful for ‘measuring the breadth of content in the curriculum. In addition, they have three other strengths: 1, They are highly reliable. Reliability, ot the lkeli- hood that candidates of similar ability levels taking a different form of the exam will receive the same scotes, is controlled more effectively with multiple- choice questions than with free-respanse questions. 2. They allow the Development Committee to clude a selection of questions at various levels of difficulty, thereby ensuring that che measurement of differences in students’ achievement is optimized. For AP Exams, the most important distinetions are between students earning the grades of 2 and 3, and 3 and 4. These distinctions are usually best ed by using many questions of middle diffculry 3, They allow the CFC co compare the ability evel of the current candidates with those from another year. A number of questions from an earlier exam are included in. che current one, thereby allowing comparisons to be made between the scores of the earlier group of candidates and the current group. ‘This information, along with other data, is used by the CEC w establish AP grades that reflect the competence demanded by the Advanced Placement Program, and that compare with earlier grades, Free-response questions on the AP Sratistics Exam require scudents to use theie analytical and ongar tional skills to formulate cogent answers. They also allow students: 1. To relate different content areas as they formulae a complete solution to a statistics or probabilicy problem. To present uncommon yet correct responses. 3. To demonsteate their mastery of stati of creativity. ics by a show Free-response and multiple-choice questions are analyzed both individually and collectively after each administration, and the conclusions are used to improve the following year’s exam. Scoring the Exam Who Scores the Statistics Exam? The people who score the fie-response section of the AP Statistics Exam ace known as “faculty consultants.” ‘These faculty consultants are experienced statistics instructors who either teach the AP course in a high school, or the equivalent course at college or univer- sity. Great care is taken to get a broad and balanced group of teachers. Among the factors considered. before appointing someone to the role are school locale and setting (urban, rural, etc.), gender, cechnicity, and years of teaching experience. If you are interested in applying to be a faculty consultant at a fueure AP Reading, you can complete and submit an ‘online application in the “Teachers” section of the AP website (wwu.collegeboard.org/ap), or request a printed application by calling (609) 406-5384. [2]During the second week of June 1997, 56 teachers of statistics, about half from colleges and half from high schools, gathered at the College of New Jersey, Trenton. Among these teachers, eight were invited to serve as “rable leaders” and to come to the Reading two days carly to help lead the effort. The remaining 48 readers were divided into eight teams of six readers each, with cach teazm ceporting to one table leader. Under the guidance of the Chief Faculty Consultan, the table leaders had responsibility for organizing the details of the Reading and conveying information to the readers in the respective teams. Ensuring Accuracy The primary goal of the scoring process is co have each faculty consultant score his or her set of papers Fairly, uniformly, and to the same standard as the other faculty consultants, This is achieved chrough the creation of detailed scoring guidelines, the thorough raining of all faculty consultants, and various “checks and balances” applied throughoue che AP Reading How the Scoring Guidelines are Created 1. Before the AP Reading, the CEC prepares a draft of the scoring guidelines for each free-response question. In the case of Statistics, 2 5-point scale (0-4) was used. A score of 0 means the student received no credit for the problem. 2. The CRC, question leaders, table leaders, and ETS content experts meet atthe Reading ste a few days before the reading begins. They review and revise che draft scoring guidelines, and test them by pregrading randomly selected student papers. The Statistics leaders were satisfied thar chis method allowed for consistent scoring of open-ended questions for which many different approaches could be equally correct and for which a written statement on assumptions and conclusions was required. If problems or ambiguities become apparent, the scoring guide- lines are revised and refined until a final consensus is reached, 3, The CEG, question leaders, and table leaders conduct training sessions for each fiee-response question, which are attended by all the faculty consultants who are scoring that question. Training Faculty Consultants to Agply the Scaring Guidelines Since the training of the faculty consultants isso vital in ensuring that students receive a grade that accurately reflects their performance, the process is chorough: 1. The faculty consultants read sample papers that have been pregraded (see above). These samples reflect all levels of abilicy. Each group of faculry consultants then compares and discusses the scores for the samples, based on the scoring guidelines. 3. Once the faculty consultants asa group can apply the standards consistently and without disagree- ment, they begin reading in teams of two. Each team member scores a packet of five papers and then exchanges the examinations for a second reading. Scores and differences in judgmenc are discussed uncil agreement is reached, with the question leaders, the rable leaders, or the CRC acting as arbitrator when needed. 4, After team shows consistent agreement on is scores, ies members proceed to score individually Faculty consultants are encouraged to seek advice from each other, the question leaders and table leaders, or the CFC when in doubt about a score. Acstudent response that is problematic receives multiple readings and evaluations. Maintaining the Scoring Guidelines A potential problem is thac a faculty consultant could give an answer a higher o lower score than it deserves because the same student has performed well or poorly con other questions. The following steps are taken t0 prevent this so-called “halo effect” Each question is read by a different faculey consultant; All scores given by other faculty consultants are completely masked; and @ The candidate’ identification information is covered, Using these practices permits each faculty consultant to evaluate free-response answers without being prejudiced by knowles individual candidates.Here are some other methods that help ensure that everyone is adhering closely to the scoring guidelines: The entire group discusses pregeaded papers exch morning, and as necessary during the day. @ Table leaders re-read (back read) a portion of the student papers from each of the readers in chat leader's eam, This approach allows each leader to guide his or her readers toward appropriate and consistent interpretations of che rubrics, & Faculty consultants are paiced, so that every reader has a partner to check consistency and to discuss problem cases with; rable leaders were also paired up to help each other on questionable calls. The CFC and the question leaders monitor use of the full range of the scoring scale for the group and for each faculty consultant by checking daily graphs of score distributions. Preparing Students for the Exam The AP Statistics course is designed to be comparable to atypical non-calculus-based introductory statistics course taught in a college or university department of math- cematics, mathematical sciences, or statistics. The outline of topies for the course was developed after careful seudy of the components of modern statistics courses taught in these venues. There are a wide variety of statistics courses taught with emphasis in business, social sciences, engineering, or other concentrations that would nor necessarily be equivalent to the AP course, although there should be considesable overlap. Thus, it is important that the student and AP teacher understand the type of college course toward which the AP course is directed. As outlined in the AP Statistics Course Description, the course emphasizes four main areas: @ Exploring Data: observing patterns and deparcures from patterns Planning a Study: deciding what and how to measure | Anticipating Patterns: producing models using probability and simulation @ Statistical Inference: firming models Compared to most equivalent college cousses, the AP syllabus is actually much more ambitious. The more comprehensive outline can be accommodated in the [AP cousse because it usually runs for a full academic yeas, as opposed to the typical single semester devoted to the course at the college level. The extra topics and depth of coverage to which the AP student is exposed prepares ‘that student for a wide variety of college courses found within the mathematical sciences arena. ‘The AP Statistics course emphasizes modern data analysis (defining a problem, designing a data coll plan, collecting data, analyzing data, and making decisions through data) rather than the theory of statistics or probability. Technology, then, has a key role to play in the learning of the subject since the computer is the chief tool for modern data analysis. Students should have some experience wish statistical sofware and be able co read standard computer printouts. Because a computer cannat be used on the exam, each student is expected to have access to a graphing caleula- tor with standard statistical functions, Some caleula- tions may be required on the exam. In the final analysis, sradents must have completed a serious course in the basics of modern statistical meth- oods and practice, with some exposure «© probability as it is used to describe statistical discributions and some experience with modern statistical technology. Even with a full year to master this material, many students will find this isa difficult agenda to complete. The developers of the AP Statistics program, knowing rhat the course is quite demanding, have tried to alleviate some of the pressure by tying key ideas to current strands in statistics that are developing throughout the K-12 mathematics curriculum. The basics of exploring, data can begin in the elementary grades, for example, and simulation as a tool to understand statistical distributions can begin in the middle grades. In chat way, statistics becomes a way of using dara to salve problems with consistent and repeating themes throughout the student’ K-12 experience. Viewed in these terms, the AP syllabus does not seem as imposing asat firs sight.Teacher Support ‘There are a number of resources available to help teachers prepare their students — and themselves — for the AP course and exam AP workshops and summer institutes. New. and experienced teachers are invited to attend work shops and seminars to learn the rudiments of teaching an AP course as well as che latest in each course's expectations. Sewsions of one day to several weeks in length are held year-round. Dates, locations, topics, and fees arc available from the College Board’s Regional Offices (see the inside front cover of this booklet), in the publication Graduate Summer Courses and Institutes, or in the “Teachers” section of our website (see below). AP's comer of College Board Online® You can, supplement your AP course and preparation for the exam with plentiful advice and resources from our AP web pages (wrnw.collegeboard.org/ap) Online discussion groups. The AP Program has developed an interactive online mailing list for each AP subject. Many AP teachers find this free resource to be an invaluable tool for sharing ideas with colleagues on syllabi, course texts, teaching rechniques, and s9 on, and for discussing other AP issues and topics as chey arise. To find our how co subscribe, go to the “Teachers” section of our website. AP publications and videos. See the Appendix for descriptions ofa variety of useful materials for teachers. ‘OF particular interest is the publication thar comple- ments this Released Exam - the Packet of 10. Teachers can use these multiple copies of the 1997 AP Statistics Exam, which come with blank answer sheets, 0 simulate a national administration in their classroom. AP videoconferences. Several videoconferences are held each year so tha AP teachers can converse elec- tronically wich the high school and college teachers who develop AP courses and exams. Schools that participate in the AP Program are notified of the time, date, and subject of the videoconference in advance. Or, you can contact your Regional Office for mare information, Videotapes of each conference are available shortly after the event; see the Appendix for ordering information.The 1997 AP Statistics Examination = Exam Content and Format Purpose of the Exam Giving a Practice Exam 1 Inscructions for Administering the Exam @ The Exam Exam Content and Format The 1997 AP Statistics Exam contained questions from all four major areas of concent (exploring data, planning a study, probability, and statistical inference) in both the 35-question objective (multiple-choice) and 6-question Free-response parts. Each part contributed 50% to the composite score. The six free-response questions covered the areas of dara exploration, study design, probability, statistical inference and fitting models to data. The first five were short-answer questions; the sixth was a longer investigative task carrying 25% of the score for the fSree-response section. Question 1. The data exploration question involved cumulative proportions, which is not adequately covered in most standard textbooks, but was based on relatively simple daca sets and asked for summary statistics and interpretations well within the content outline for this course. Question 2, The design question asked students t0 explain how they would sev up an experiment, and a complete response required explanation of both block- ing and randomization, ‘Question 3. The probability question required some knowledge of conditional probability bur the answers could be found through logical thinking without appeal «0 formal theorems on probability. Questions 4 and 5. The two inference questions were buil around scenarios that required the comparison of ‘wo proportions and the analysis of che mean of paired differences, respectively. These questions were similar to the typical questions found in textbooks and, hence, generated extensive responses from almose all students taking the exam, Question 6. The investigative task required the student t0 critique models already fit to a ser of daca and then to find a model that did not have the weak- nesses of those presented. For this question, students possessing skill wich a graphing calculator may appear to have had some advantage over others, but this was offier by a grading scheme that gave as much weight to 4 good explanation as to clever calculation. The scoring guidelines for the free-response ques tions, and sample student responses, can be found in Chapter IIL Purpose of the Exam The purpose of che AP Statistics Exam is to allow students to demonstrate mastery of the concepts and techniques of modern statistics at the level of a non- calculus-based inssoductory college course. Such a course is required or recommended for most college majors and, in fact, the numbers of scudents taking introductory statistics is rapidly approaching the number taking calculus. Ifa student earns a satisfactory AP grade and consequently credit for the equivalent college course, chen thae student may have the opportu- nity 10 take a second statistics course that will provide the special emphases requited of his or her major. Even if no second course is in the offing, the student is prepared to confront statistical issues much earlier in the college progeam than miight otherwise be the case. Scudents who take the AP Statisties course but ope not to take the exam still have the advantage of background knowledge that will serve them well when they do take statistics as part of their college pragsam of studies. The above discussion begs the question, “what is the purpose of such a college course?” Students of roday, the workforce of tomorrow, live in an informa- tion age. Most aspects of their lives, from the faod available to eat to che medications available for an illness, from decisions about buying a car co decisionsabout choosing an occupation, from choices of political candidates to choices of movies or TV programs, are regulated by data that they or someone else has col- lected and analyzed, for good or ill. Therefore it behooves students to learn something about daca collection and analysis so that they can enjoy life as informed citizens and productive workers. Numeracy, being able to “read” and understand data, is now as important as literacy. In addition to the advantages for life enhancement, introductory statistics provides the basis for the deeper study of the subject required in many fields, including medical science, biology; engi- neering and psychology. AP Statistics is a good option for any student, but particularly for a student who plans farcher study in a quantitative field. Giving a Practice Exam ‘The following pages contain the instructions, as printed in the 1997 Coordinator's Manual, for administering the AP Statistics Exam. Following these instructions is a copy of the 1997 Statistics Exam. If you wish to use this released exam to test your students, you may wish to use the instructions to create an exam situation that closely resembles @ national administration. If so, read only the rections in the boxes to the students; all other instruc- tions are for the person administering the test and need not be read aloud. Some instructions, such as those referring to the date, the time, and page numbers, are no longer relevant; please ignore them. Another publication that you might find useful is che so-called “Packets of 10.” They are just chat: packets of en of the 1997 AP Statistics Exam, each with a blank answer sheet. For ordering information, sce the Appendix.Instructions for Administering the Exam the Sites Beaman Betas eg ie xa sininoran, take sure senha laplop o Sther portable conpster poste ganze, dvi with typewriter-style (QWERTY) keyboard (HP-95, T10Ge) cron wring edo en np device (Nowtom ste) Its canigate has toch 3 ict docsothavealeultorfh sacl carats you may ive he candidate one fom your supply Ifa candidate does not want 0 use the || verlag you have proved ave him or her we under “Calculators” in the “Administering the Exam” section. Candidates may have one or two calculators, fon their desks while Sections T and I are being administered. Candidates with Hewlett Packard 48 Series graphing calculators may use cards designed for use with these calculators, Proctors should make sure infrared ports (Hewlett Packard) are not sarroreces each other. Section I of your test contains only nuitiple- choice questions. Questions in Section I are numbered 1 through 35, Mark your responses on page 2of your answer sheet. You are not to open the sealed Section IT booklet until you are told to doso. Remember, when you come to the end of the multiple-choice questions, there will be answer ovals left on your answer sheet. The time for Section 1 is 90 minutes. Scratch paper is not | allowed but you may use the margins of your Section I booklet. Are there any questions? Answer all questions regarding procedure. Set your watch at 12:59. When it reads exactly 1:00 sa ‘Open your Section I booklet and begin. While the candidates are working, you and your proctors should make sure they are marking their answers on page 2 of the answer sheet in pencil. The color of page 2 of the answer sheer is purple (blue for late administrations). Calculator memories need not be cleared before or after the exam, Calculators may not be shared. Communication between calculators is prohibited during the exarn. Proctors should walk around and make sure Hewlett Packard calculators’ infrared ports are not facing each other p> Undertned instructions should not be read aloud during ‘a hte administration, AT 2: If you are using these instructions. == scheduled exam, disregard all instructions marked with an arrow (>), Ifyouare using these instructions for alate administration, read them carefully beforehand, keeping in mind the following: 1) directions marked with an arrow (B>) apply only to proctors giving late administrations; 2) underlined. instructions should nor be read to candidates during a late administration; 3) dates and days to be read aloud during a late administration should be adjusted as necessary. ‘After completing the general instructions beginning on page 31, say: 0 PM — Stop working, Close your exam booklet. Make sure you printed your name, last name first, on the {cont cover of your Section I booklet. ... Do not insert your answer sheet in the booklet. I will now collect the answer sheets. After you have collected an answer sheet from every candidate, say It is Tuesday afternoon, May 6, and you will | | be taking the AP Statistics Exam, You may not use reference materials or unapproved calculators during this examination, If you brought any with | ‘you, put them under your chair. Print your name, last name first, on the front cover of the unsealed Section I booklet. . .. Read the directions on the back of the booklet. When you have finished, look _ _ ee Seal the Seton 1 bookie with the three seals] you have provided the information requested and ‘marked your responses correctly. ... Your answer provided. Pull off each seal from the backing sheet the area marked “PLACE SEAL HERE.” Fok Shectilesonedby machine orn | ‘may alter your grade. Mark your responses on | page 2 of your answer sheet (one response per | | and press it on the front cover so it just covers ‘over the open edge and press it to the back cover. Use one seal for each open edge. Be careful not to let the seals touch anything except the marked question). Be certain the number of the question areas... you are answering matches the number on the answer sheet, Use only no. 2 pencils to mark your answers on Section I. Your answer marks must be dark and fill the oval completely. Stray marks and smudges may be read as answers by the machine so erase carefully and completely. Be sure Collect the sealed Section 1 exam booklets. yon receive one from every candidate; then give your ibreak instructions. A five-minute break is permitted, Students may talk, move about, or leave the room together to get a drink of water or go to the rest room. Caleulators ‘must remain turned off and must NOT be taken from the examination room. (See “Breaks During the Examination”) D> Late Testing Only 4GIVE YOUR BREAK INSTRUCTIONS. ‘After the break, say ‘Open the package containing your Section IT booklet. Turn to the back cover of the booklet, and read the instructions at the upper lef your identification information, in penci boxes... Taking care not to tear the sheet beneath the cover, detach the perforationat thetop.... Fold the Gap down, and moisten and press the ghie strip firmly along the entire lower edge. .. . Your ‘identification information should now be covered and will not be known by those scoring your answers. Read the instructions at the upper right of the back cover. Print your initials in the three boxes provided. . . . Next, take two AP number labels from your Candidate Pack and place them in the two bracketed areas, one below the instructions and one tothe left. Ifyou don’t have numberlabels left, copy your number from the back cover of your Candidate Pack within both of the bracketed areas. ... Item 6 provides you with the option of ig Educational Testing Service permission to use your free-response materials for educational research and instructional purposes. Your name would not be used in any way with the free- response materials. Read thestatementandanswer either “yes” or “no”... Are there any questions? Answer all questions regarding procedure, Then say: It you wilt he taking another AP Examination, I will collect your Candidate Pack. You may keep ‘your Candidate Pack if this is your last or only AP examination. Collect the Candidate Packs. Then say: If you are administering the alternate form of the examination for a late administration, DO NOT read the underlined portions in the following (wo boxes. Read the directions for Section [f on the back of your booklet. Look up when you have finished... Youmayuse the insert for scratchwork, but_be sure to show your work and write your answers jn the Section 11 booklet, No credit will be given for work shown in the insert, If you need ‘more paper, raise your hand. Are there any questions? D Late Testing Only Answer all questions regarding procedure. Set your watch at 2:29. When it reads exactly 2:30, say’ Open the Section II booklet, Tear out the insert in the center of the booklet. ... Print your name on tte upper left-hand commer. willbe collecting the insert at the end of the administration. 1¢ will be returned to you tomorrow by your teacher... Begin work on Section II. ‘You and yourproctors should check to be surealf candidates ‘are writing their answers in the Section II booklets. AT 4:00 — [Stop working, Close your Section II booklet and Keep it closed on your desk. I will now collect your booklets. Remain in your seats, without talking, while the exam materials are being collected. Collect the Section If booklets and the green inser. The alternate exam for late administrations does not have an insert Be sure you have one of each from every candidate Check theback ofeach bokletto make sure the candidate's [AP number appearsin the two boxes. When all examination rmateriis have been collected, dismiss the candidates. The teen inserls may be given tothe appropriate teacher for return to the students the fitst school day after the administration. Fill in the necessary information for the Statisties Examinations on the appropriate S&R Form. ‘Alternate exams should be recorded on their respective tine on the SER Form, (Only altemate exams have an item number listed in the column labeled “Item Number”) Put the exam materials in locked storage until they are resumed to ETS in one shipment after your school’s last Administration. See “Activities After the Exam.STATISTICS A CALCULATOR MAY BE USED IN BOTH SECTIONS OF THE EXAMINATION, CALCULATORS MAY NOT BE SHARED. REFERENCE MATERIALS MAY NOT BE USED. “Three hours are allowed for this examination: 1 hour and 30 minutes for Section I, which consists of multiple- choice questions, and | hour and 30 minutes for Section II, which consists of longer problems. In determining ‘your grade, the (wo sections are given equal weight. Section I is printed in this examination booklet; Section If, in a separate booklet SECTION I Time— 1 hour and 30 minutes Number of questions —35 Percent of total grade—50 Section I of this examination contains 35 multiple-choice questions. Please be careful to fill in only the ovals ‘that are preceded by numbers 1 through 35 on your answer sheet. General Instructions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE INSTRUCTED TO DO SO. INDICATE ALL YOUR ANSWERS TO QUESTIONS IN SECTION | ON THE SEPARATE ANSWER SHERT ENCLOSED. No credit will be given for anything written in this examination booklet, but you may use the booklet for notes or scratchwork. After you have decided which of the suggested answers is best, COMPLETELY fill in the corresponding oval on the answer sheet. Give only one answer to each question. If you change an answer, be sure that the previous mark is erased completely. Example: What te artes mean ofthe numbers Sample Answer 1 Mt Ms O38 10 1 OF Oz Many candidates wonder whether or not to guess the answers to questions about which they are not certain. In this section of the examination, as a correction for haphazard guessing, one-fourth of the number of questions you answer incorrectly will be subtracted from the number of questions you answer correctly. It is improbable, therefore, that mere guessing will improve your score significantly; it may even lower your score, and it does take time. If, however, you are not sure of the best answer but have some knowledge of the question and are able 10 climinate one oF more of the answer choices as wrong, your chance of answering correctly is improved, and iC may be 0 your advantage to answer such a question Use your time effectively, working as rapidly as you can without losing accuracy. Do not spend too much time cn questions that are too difficult. Go on to other questions and come back zo the difficult ones later if you have time. It is not expected that everyone will be able (0 answer all the multiple-choice questions. Formulas begin on page 12. ‘Questions begin on page 15. “Tables begin on page 34. CCopysghe © 1997 by Educational Testing Service and College Entrance Examination Board ll ight served 11Formulas () Descriptive Statistics (m4 =I) si +(m ~1)s5 (m=1)+(%2=1) Sp Sado thx(I) Probability PAU B)= P(A)+P(B)- (ANB) P(AQB) MA E(X)= py = Lapp; Var(X)= 07 = D(a ~ Hx) IfX has a binomial distribution with parameters n and p, then: roc==[f)pta- pt IfX has a normal distribution with mean p. and standard deviation 6, then: be =h o op= vn(HM) Inferential Statistics . , estimate — Standardized test statistic: imate — parameter standard deviation of estimate Confidence interval: estimate + (critical value) + (standard deviation of estimate) Single-Sample Proportion Two-Sample Difference of means 2 ge {unequal variances) C1 4, 92 m M2 Difference of means Tt (equal variances) Olay Say Difference of proportions i 1 (unequal variances) it mn Po alcnl Difference of proportions fap fo (equal variances) P(l-P) yn tn served 2 Chi-square test statistic = y, Cnet epeeSTATISTICS SECTION Time—1 hour and 30 minutes Number of questions—35 Percent of total grade—50 Directions: Solve each of the following problems, using the available space for scratchwork. Decide which is the best of the choices given and fill in the corresponding oval on the answer sheet. No credit will be given for anything written in the test book. Do not spend too much time on any one problem, 1. USA Today reported that speed skater Bonnie Blair had “won the USA's heart,” according to a USA Today/CNNIGallup poll conducted on the final Thursday of the 1994 Winter Olympics. When asked who was the hero of the Olympics, 65 percent of the respondents chose Blair, who won five gold medals. The poll of 615 adults, done by telephone, had a margin of error of 4 percent. Which of the following statements best describes what is meant by the 4 percent margin of error? (A) About 4 percent of adults were expected to change their minds between the time of the poll and its publication in USA Today (B) About 4 percent of adults did not have telephones. (C) About 4 percent of the 615 adults polled refused to answer. (D) Not all of the 615 adults knew anything about the Olympics. (E) The difference between the sample percentage and the population percentage is likely to be jess than 4 percent. CCR Oa ae Ct 152. An automobile manufacturer claims that the average gas mileage of a new model is 35 miles per gallon (enpg). A consumer group is skeptical of this claim and thinks the manufacturer may be overstating the average gas mileage. If [L represents the true average gas mileage for this new model, which of the following gives the null and alternative hypotheses that the consumer group should test? (A) Hy: Hi, ®) Hy: Hy: © Hy it (D) Hy: Hy (E) Hy H: H< 35 mpg 1 2 35 mpg S35 mpg > 35 mpg b= 35 mpg b> 35 mpg H = 35 mpg a < 35 mpg w= 35 mpg ht # 35 mpg 3. A magazine has 1,620,000 subscribers, of whom 640,000 are women and 980,000 are men. Thirty percent of the women read the advertisements in the magazine and 50 percent of the men read the advertisements in the magazine. A random sample of 100 subscribers is selected. What is the expected number of subscribers in the sample who read the advertisements? (A) 30 B) 40 (©) 42 (D) 50 (E) 80 TCR a amt4. A manufacturer makes lightbulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company’s claim is correct, what is the expected number of nondefective lightbulbs in a random sample of 1,000 bulbs? (A) 20 (B) 200 (©) 960 (D) 980 (E) 1,000 5. When a virus is placed on a tobacco leaf, small lesions appear on the leaf. To compare the mean number of lesions produced by two different strains of virus, one strain is applied to half of each of 8 tobacco leaves, and the other strain is applied to the other half of each leaf. The strain that goes on the right half of the leaf is decided by a coin flip. The lesions that appear on each half are then counted. The data are given below. Leaf Strain? Strain 2 1 31 18 2 20 7 3 18 14 4 7 HW 5 9 10 6 8 1 7 10 3 8 7 6 What is the number of degrees of freedom associated with the appropriate t-test for testing to see if, there is a difference between the mean number of lesions per leaf produced by the two strains? (A) 7 (B) 8 © i (D) 14 (E) 16 GO ON TO THE NEXT PAGE 176. Which of the following is a criterion for choosing a t-test rather than a z-test when making an infer- ence about the mean of a population? (A) The standard deviation of the population is unknown. (B) The mean of the population is unknown, (C) The sample may not have been a simple random sample. (D) The population is not normally distributed. {E) The sample size is less than 100. 7. A certain county has 1,000 farms. Corn is grown on 100 of these farms but on none of the others. In order to estimate the total farm acreage of corn for the county, two plans are proposed. Plan I: (a) Sample 20 farms at random. (b) Estimate the mean acreage of corn per farm in a confidence interval. (c) Multiply both ends of the interval by 1,000 to get an interval estimate of the total. Plan II: (a) Identify the 100 corn-growing farms (b) Sample 20 corn-growing farms at random. (c) Estimate the mean acreage of corn for corn-growing farms in a confidence interval. (4) Multiply both ends of the interval by 100 to get an interval estimate of the total. On the basis of the information given, which of the following is the better method for estimating the total farm acreage of corn for the county? (A) Choose plan I over plan I. (B) Choose plan II over plan I (©) Choose either plan, since both are good and will produce equivalent results (D) Choose neither plan, since neither estimates the total farm acreage of corn. (E) The plans cannot be evaluated from the information given. UO a sama 18Eee 8. Which of the following can be used to show a cause-and-effect relationship between two variables? (A) A census (B) A controlled experiment (C) An observational study (D) A sample survey (E) A cross-sectional survey 9. To check the effect of cold temperature on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a freezer for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before breakage is measured on each rubber band, and the mean for the cold bands is compared to the mean for the others. Is this a good experimental design? (A) No, because the means are not proper statistics for comparison. (B) No, because more than two brands should be used (C) No, because more temperatures should be used. (D) No, because temperature is confounded with brand, (B) Yes GO ON TO THE NEXT PAGESet A SetB = ———| — 10 20 30 40 50 10. The boxplots above summarize two data sets, A and B. Which of the following must be true? I. Set A contains more data than Set B. IL. The box of Set A contains more data than the box of Set B. TIL. The data in Set A have a larger range than the data in Set B. (A) Lonly (B) I only (©) Land II only (D) Mand IIT only (©) 1M, and I 11, The XYZ Office Supplies Company sells calculators in bulk at wholesale prices, as well as individu- ally at retail prices. Next year’s sales depend on market conditions, but executives use probability to find estimates of sales for the coming year. The following tables are estimates for next year’s sales. WHOLESALE SALES Number Sold 2,000 5.000 10,000 20,000 Probability or 03 04 02 RETAIL SALES Number Sold 600 1,000 1,500 Probability 04 0s 0.1 What profit does XYZ Office Supplies Company expect to make for the next year if the profit from each calculator sold is $20 at wholesale and $30 at retail? (A) $10,590 (B) $220,700 (©) $264,750 (D) $833,100 OR Gan ada \c3 (B) $1,002,50012. The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is closest to (A) 60 (B) 62 © 68 ) 70 (E) 74 13. Joe and Matthew plan to visit bookstore. Based on their previous visits to this bookstore, the proba- bility distributions of the number of books they will buy are given below Number of books Joe will buy 0 I Probability 050 0.25 0.25 Number of books Matthew will buy 0 1 2 Probability | 0.25 0.50 0.25 Assuming that Joe and Matthew make their decisions independently, what is the probability that they will purchase no books on this visit to the bookstore? (A) 0.0625 (B) 0.1250 (C) 6.1875 (D) 0.2500 (E) 0.7500 Cn Cam 21Job NoJob Total Juniors [13 5 18 Seniors | 13 26 39 Total 26 31 37 14, A survey of 57 students was conducted to determine whether or not they held jobs outside of school. The two-way table above shows the numbers of students by employment status (job, no job) and class Guniors, seniors). Which of the following best describes the relationship between employment status and class? (A) There appears to be no association, since the same number of juniors and seniors have jobs. (B) There appears to be no association, since close to half of the students have jobs. (C) There appears to be an association, since there are more seniors than juniors in the survey. (D) There appears to be an association, since the proportion of juniors having jobs is much larger than the proportion of seniors having jobs. (E) A measure of association cannot be determined from these data 3 CSC«SSSC«SSCS 15. Which of the following is the best estimate of the standard deviation of the distribution shown in the figure above? (A) 5S (B) 10 (C) 30 (D) 50 (E) 60 Ce an aa 2216. Ten students were randomly selected from a high school to take part in a program designed to raise their reading comprehension. Each student took a test before and after completing the program. The mean of the differences between the score after the program and the score before the program is 16. It was decided that all students in the school would take part in this program during the next school year. Let 11, denote the mean score after the program and H, denote the mean score before the program for all students in the school. The 95 percent confidence interval estimate of the true mean difference for all students is (9, 23). Which of the following statements is a correct interpretation of this confi- dence interval? (A) by > Hp with probability 0.95. (B) Lt, 14, the sample result is quite likely. (E) For any 1, and py with 9 < (1, — Hy) < 23, the sample result is quite likely. 17. Gina’s doctor told her that the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.50. Which of the following is the best interpretation of this standardized score? (A) Gina’s systolic blood pressure is 150. (B) Gina’s systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age. (C) Gina’s systolic blood pressure is 1.50 above the average systolic blood pressure of women her age. (D) Gina’s systolic blood pressure is 1.50 times the average systotic blood pressure for women her age. (E) Only 1.5% of women Gina’s age have a higher systolic blood pressure than she does. Cee al am ti18, The Physicians’ Health Study, a large medical experiment involving 22,000 male physicians, attempted to determine whether aspirin could help prevent heart attacks. In this study, one group of about 11,000 physicians took an aspirin every other day, while a control group took a placebo. After several years, it was determined that the physicians in the group that took aspirin had significantly fewer heart attacks than the physicians in the control group. Which of the following statements explains why it would not be appropriate to say that everyone should take an aspirin every other day? 1. The study included only physicians, and different results may occur in individuals in other occu- pations. II. The study included only males and there may be different results for females. TM. Although taking aspirin may be helpful in preventing heart attacks, it may be harmful to some other aspects of health. (A) Lonly (B) only (©) Wonly (D) I and TI only (E) 1,11, and Ut CO an 2 aa.| 24Questions 19-20 refer to the following information, Every Thursday, Matt and Dave's Video Venture has “rofl-the-dice” day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and a two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the stan- dard deviation of X is $0.15. 19. If a customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies? (A) $0.45 (B) $0.47 (C) $0.67 (D) $3.00 (E) $9.40 20. If a customer rolls the dice and rents a second movie every Thursday for 30 consecutive weeks, what is the approximate probability that the total amount paid for these second movies will exceed $15.00 ? (A) 0 (B) 0.09 (© 0.14 (D) 0.86 (E) 0.91 Cea 2 a(t 2521. A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made? (A) Mean (B) Median (C) Mode (D) Range (B) Variance 22. ‘The back-to-back stem-and-leaf plot below gives the percentage of students who dropped out of schoo! at each of the 49 high schools in a large metropolitan schoo} district. Schooi Year School Year 1989-1990 | 1992-1993. ols 9999887/0|566677788899 4444433222211110/1}o0001111222334444 9997766665/1|555666677778 4222100/2|13 8887 6/2 2S e(Ontgsi 2) 766) 35 4 For 1992-1993, 1|2 represents 12% Which of the following statements is NOT justified by these data? (A) The drop-out rate decreased in each of the 49 high schools between the 1989-4990 and 1992-1993 school years. (B) For the school years shown, most students in the 49 high schools did not drop out of high school. (C) In general, drop-out rates decreased between the 1989-1990 and 1992-1993 school years. (D) The median drop-out rate of the 49 high schools decreased between the 1989-1990 and 1992-1993 school years. (E) The spread between the schools with the lowest drop-out rates and those with the highest drop-out rates did not change much between the 1989-1990 and 1992-1993 school years. TRC a aes23. Circuit boards are assembled by selecting 4 computer chips at random from a large batch of chips. In this batch of chips, 90 percent of the chips are acceptable. Let X denote the number of acceptable chips out of a sample of 4 chips from this batch, What is the least probable value of X 7 (A) 0 (B) 1 © 2 (D) 3 4 24. A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $127.95 and a standard deviation of $24.03. If the size of this sample is 40, which of the following is an approxi- ‘mate 90 percent confidence interval for the average cost of a repair at this repair shop? (A) $127.95 + $4.87 (B) $127.95 $6.25 (C) $127.95 £ $7.45 (D) $127.95 + $30.81 {E) $127.95 £ $39.53 2725. Ata college the scores on the chemistry final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the chemistry final and 84 on the calculus final. Relative to the students in each respective class, in which subject did this student do better? {A) The student did better in chemistry. (B) The student did better in calculus. (C) The student did equally well in each course. (D) There is no basis for comparison, since the subjects are different from each other and are in different departments. (E) There is not enough information for comparison, because the number of students in each class is not known. 26. A fair coin is flipped 10 times and the numiber of heads is counted. This procedure of 10 coin flips is repeated 100 times and the results are placed in a frequency table, Which of the frequency tables below is most likely to contain the results from these 100 trial (A) Number of | Frequency (B) | Number of | Frequency (©) Number of | Frequency Heads Heads Heads 0 19) 0 9 [0 0 1 12 i 9 1 o 2 9 2 9 2 | 6 E} 6 3 9 3 9 5 1 5 10 5 24 6 3 6 9 6 18 7 5 7 9 7 12 8 8 L 8 9 8 7 14 9 9 9 2 10 2 J 10 9 10 0 (DP) Number of | Frequency | ©) [ Number of | Frequeni Heads 1 _ 10 0 2 6 i} 4 8 24 5 10 St |__6 9 22 7 12 1 10. 9 oO27. The student government at a high school wants to conduct a survey of student opinion. It wants to begin with a simple random sample of 60 students. Which of the following survey methods will produce a simple random sample? (A) Survey the first 60 students to arrive at school in the morning. (B) Survey every 10th student entering the schoo! library until 60 students are surveyed. (C) Use random numbers to choose 15 each of first-year, second-year, third-year, and fourth-year students. (D) Number the cafeteria seats. Use a table of random numbers to choose seats and interview the students until 60 have been interviewed. (E) Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey. 28. There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of some data collected by a biologist gives the model j= 25.2 + 3.3 9 10, a sample from a normal population produces a mean of 13.4, The z-score for the sample is'2.12 and the p-value is 0.017. Based on these statistics, which of the following conclusions could be drawn? (A) There is reason to conclude that [L > 10. (B) Due to random fluctuation, 48.3 percent of the time a sample produces a mean larger than 10. (C) 17 percent of the time, rejecting the alternative hypothesis is in error. (D) 17 percent of the time, the mean is above 10. (E) 98.3 percent of the time, the mean is below 10. 30. For which of the following distributions is the mean greater than the median? (A) 0 (@B) 0 © 0 —_ _ (D) ® <—— FN CRC a aa. (3 30Hew euare 012345678 31. The equation of the least squares regression line for the points on the scatterplot above is, y = 1.3 + 0.73x. What is the residual for the point (4, 7)? (A) 2.78 (B) 3.00 (C) 4.00 (D) 4.22 (E) 7.00 32. The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10 percent of the loaves weighed Jess than 15.34 ounces, and 20 percent of the loaves weighed more than 16.31 ounces. What are the mean and standard deviation of the distribution of the weights of the loaves of bread? (A) w = 15.82, (B) p = 15.82, (©) p= 1587, D) w= 15.93, (E) » = 16.00, COC ans aac33, A 9S percent confidence interval of the form + E will be used to obtain an estimate for an unknown population proportion p. If 6 is the sample proportion and E is the margin of error, which of the following is the smallest sample size that will guarantee a margin of error of at most 0.08 ? ia) 25 (B) 100 © 175 (D) 250 (E) 625 34, The process of producing pain-reliever tablets yields tablets with varying amounts of the active ingre- dient. It is claimed that the average amount of active ingredient per tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample of 70 tablets. The mean content of the active ingredient for this sample is 194.3 milligrams, while the standard deviation is 21 milligrams. What is the approximate p-value for the appropriate test? (A) 0.012 (B) 0.024 (C) 0.050 (D) 0.100 (E) 0.488 On Cra aa 3 3235. A survey was conducted to determine what percentage of college seniors would have chosen to attend a different college if they had known then what they know now. In a random sample of 100 seniors, 34 percent indicated that they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who would have attended a different college is (A) 24.7% to 43.3% (B) 25.8% to 42.2% (C) 26.2% to 41.8% (D) 30.6% to 37.4% (E) 31.2% to 36.8% END OF SECTION I IF YOU FINISH BEFORE TIME IS CALLED, YOU MAY CHECK YOUR WORK ON SECTION I DO NOT GO ON TO SECTION II UNTIL YOU ARE TOLD TO DO SO. 33Table entry for zis the probability lying below 2 Probability ‘fable A Standard normal probabilities 5 or o 08 10099 oon r 00% 0098 (009100890087 0084 01250122, 9191160113110 162 01884 31923156 3363235943557 35203483, 4013 3974 393638973859 44044364 ass 4864247 490147614721 46814641Probability Table entry for zis the probability lying below Table A (Continued) z | ot 02 3 0s 96 0 08 09 5000 504050805120 S160 519952305279 S319 5359 5398 5438 S478_ 5517553575596 S686 5675 S714 5753 5793 3832 587159105948 598760266064 ©6103. 6141 6179 “621762556293. 633163688406 GAS 4806S 6554 659166286654 67006736. 6772__—6ROB_—_ 844.6879 69156950 019° -70sa° 0887193 7157/7190 yaa ms1 791 T5179 ganas 7a TST. 7549 | 7580. T61l 1673 T0474 TGA 778237852 7881-7910 967-7905 302380518078 81058133, "R159 8186 8238 Sieh 8289 TIS BO 83658389 B13 8438 MG] 848585088532 85S4— 8577859861 613 (8665-8686 “8708878749 8TI0.—«« 8790810830, 8849 8869 ©—«-8BBB_ 8907 «892580448962 8980-8997 9015 9032 9049-9056 9082-9099 911s. 913191479162 9177 919292079222. 936 925192659279 9282-9306. 9319 9332/7 9MS" 9357 9370-9382) 93049406948 9429 gaan 9452 946394749484 4959505 9S1S. 95255359545 9554 9564 957S_—«9SBZ_—«85SS]_— 939996089616. 962S.— 9633, 2641 964996569664 967196788686 «96936999706 S13 99-96 9732-8738 9TH 8750. 9756-76. 9767 972 ST78.—S«97RB_=«9TBS «97939798 «9803. 9808.-—=—«9812.—BIT 9821 (982698309834 983K 9BAZ~— 985 = 98SO 9854 BRST 9861 9864 986898719875 98TR 98K] 9BR4 98879890 9893 9896-9898 9901 9903-9906 9909991] 99139916. 5918 992099229925. 99279929 993199329934 ‘9936 9938") 9540" “99419943 9943/9946 99489949. 9951 9952 995399559956 99579959 996098619962 9963964 9365 9966 9967996899609) 9071987299738 9974 9971598169977, 997T = gaT8 997999799980 gat 9987 9987 998T 9988-9988 998999899989 99909900. 9990 9991-9991 99919992 9992-9992 999299939993 9593 9903 9984 994 9904 "9904 9904 990599959905, 9995 99959995 9996 9996 19995 9996 999699969997 99979997 999799979997 9997 9997 99979997 ___ 9908 35Table entry forp and Cis the point * with Probability p probability p ying above itand probability C lying _-~ between -r* and ¢*, = Table Bt stribution critical values a [asa OCS SSCS CSS 1 | 10001376 196 3078 631812711589 S12 63651273 «31836366 2 | ‘sis toi 1.38 18862920 43034849 66599251409 22.33 31.60 3 | es 9781250 16382353, 382 34824545881 745310211292 4 | 7 ou 1901533, 232-2776 29993747 60455987173 8.610 5] 779001136176 2015__ asm 2.757 336540324773 5.893 6.369 6 | © 71a 906! 71.134 Pinan a.94s” eh zaa7i aera a.us9! 3700 417 5.208 5.959 7 | "i s96 41194415195 23632517 2998 34894009 ATs 5.408 | 700 889 08139718) 2306 2928963355389 4501 5.0u1 9 703 883 1.100. 1383 ‘1.833 (2.262 2.398 2821 3.250. 3.690 4.297 4.781 10 | 700979 108332 ABI2. Dak asso 26h 36) SRL a 4ST ni | ‘607876 Loss 1363«1.796 22012398 «271831063497 das 4437 12 | 6s (873, 10831356 1782-2179 23032681 3.055 3428 3.900318 1b] os 870 Lom 13507712460 nae 2650 301233 385242 14 | 692 Rok 10761345761 -214s_ 226 ©2624-2977 332637874140 15 | ool 865 ors 1341753 2131 2.249 2.602 2.947 3.286 3.733 4073 16] 690°) 865° alone 1.337 L746 ?a.na0) 92.038 Pl 2.se3 729m" 252! S96 AIS I 689 863 1.069. 1.333 1740 2110 2224 2.567 2.898 32 3.646 3.965 1 | 688-862 106743301734 210) 22142552 2a 373613902 19 | 668 861 1.066. 3281292020539 RG] ST9 3.88 20 687 860° 1.0064 1.325 «1.725 2086 2.197 2528 BAS ‘3153 3.552 3.850. 21 | ‘ei 859 106313231721 2080-«2MRDDSIS. 28313135 35273819 mz | ‘86 858 1.061 1321«717«2.074-«2183 25082893119 35053792 a | 685 858 1060 131917142069 2177-2500 2807 3.l0s 3.853.708, 24 | as 571.059 1318 L711 2064 «-2472—«-2a92—«-2.797 3081 34673745 2 | 684 856 Lose 1316 1708 206021672485 2.787 3.078 3.450 «3.725 36 | e349 case: /alasa’ iis) 1.706 2056 72.162") 72479") 2'779"" 3.067! 3.a5 °° 3707 a | oe ass 1087 131s 17032052 2158 247s T3057 3.421 3.680 ag | (83 55 40861313720 2154 a6?) 2763 3.073.408 3.674 29 | 663 AS41055, 1311_«1699 2085-2150 24622759 «33386359 30 | 6838580581310 1697208 2a? 24572750 3.000 3.385 3646 wo | 6s 85110501303, 68420212123. «2423 «270429713307 31 50 | 61 4910471299 1.676 20091092403 2678 2.937 3.261 3.486 co | 67 ‘4810651296 L671 2000-2089 2390-2600 2.015,««3.282 3.460 so | 678 846 1.063 1252 1.664 ©1950 2088234 ©2639-2887 3.195316 100 | 677 ‘s45— 1.062120 1.660 «1988 ©2081 23k ©2625 2B 3178 3.390 wooo | 675 ‘s42 0371282 Noyes ©1962-2056 2330-2581 2.813. «3.083.300 co | 678 BH 103612821685 1960 2058-2326 ©2576 «2807-3081 3.291 50% 60% 10% «Wh ~—«UH~=«C«SS«S=*C«CK SCR «CO «CNS «SBA 09.9 Confidence level C 36‘Table entry for p is the point (22) with probabitty plying above Table Cx? critical values Probability p TL Tai probabiy p af mas Sms OSS —oo_—005 | 12460207 21 sae sm —Sal66)—~—«788~—«ONe—o ada 2 | 277 am 37 615990738782, -921 0609813821520 2 { 4 fe Sm 62s a 935 oak Mae ata? 73 4 | 539 599 e778 94d ade? 1328 1486 Nea? 8A? 2000 s | 6s 729 $12 924 107 a3 1505 167518382051 -22.1 Gf 56 94s ane 289. saas West?) 1855-2025 2046 2410 7 | gor 980 1075 2m 407 te) ies 2028 aor a2 & | 022 nm am B36 551 753 m0 2195 a8 5 | 19 224 1339 Meek 1692) i902 InGk 216725925 a8 2987 19 | 1255 tas ass 599 IRs] 048 ade a2tast9 95912 un | a7 ies 1577 1728198 age ee DAT = 267628733126 Ia 1 | i4as 1581 69918582108 2338 eos 2622283303221 1 | i598 te58 1820 1981 22362424 sa? 716 BADR 1 | iraz Bas 1941 210623682612 2687 891323343 sa SELL is | teas 1931 2060 2281 25002749 R26 50SE 32804983770 3872 4g faga7) /a0g7 (21790 2386" 2530, 2Ras’ Goea) S00!) 3427) 3646") 925 aL 0 | a ist ase 247) 759 OID gD «BAL 3572 Tas’ oT as me | 2160 758 16 25992887153 35 ALIS 381 Aha ww | mm moo 3593 270 302s 8) 361 ASR ome ne? 4897 20 | mas as08 3650. hat uai7) ism 37S? M000 2a sat 4750 a | 2493 2617 766 2962 SST 3548 gad RAIA TB “901 mn | aor 77130 war 30892676 4029 AD 5.20 5051 2 | mie 3843 998 32.01 3517 RO HSIT Los aI 682 5200 aa | 2826 2955 3113 3320 364239364027 2984556 aR she as | 29a 306 3228 3438 3765 4065 N57 ST 4693 apa 495 26())| fanaa) 31.79. 3349) 9556)-9 93RD! “4192” alas as.64)”)/aR2D." sos 561 a | ass 3291 us? 3674 Holl aI 4696 ak Sa 5786 % | 2O Mos As 2 48h MG HIE SSD 5359 5930 2» | Bn 3518 X68 90 56 as He SAT e073 30. | 34803625) 3199, ozs 437746984796. 5089 SRST. 5633 2.16 a | 4s 4727 aos Stal 5516 59.34 669657769. 7605 so} $633 S816 603s. 6317750142 Wis 949 82.6 956 6 | coos Gas7 71347440 7908 83:30 $838 91959538 9m 1027 so | se13 Gosi 9311 9658 101906 M23. 163190) f2e# 1283 voy | ost yyy 118s 124396 i558 4021443 gpa 1552 37STATISTICS SECTION Il Time—1 hour and 30 minutes Number of problems —6 Percent of total grade—50 GENERAL INSTRUCTIONS ‘There are two parts to this section of the examination. Part A consists of five equally weighted problems that represent 75 percent of the total weight of this section. Spend about 65 minutes on this part of the exam. Part B consists of one longer problem that represents 25 percent of the total weight of this section. Spend about 25 minutes on this part of the exam. Since it is not expected that everyone will be able to complete all parts of all problems, you may wish to look over all the problems before you begin to work. The questions are printed in the booklet and on the green insert: it may be easier for you to look over all the problems on the insert. Statistical tables and useful formulas are printed in the green insert. When you are told to begin, open your booklet, carefully tear out the green insert, and start work. * You should write all work far each part of each problem in the space provided for that part in this booklet. Be sure to write clearly and legibly. If you make an error, you may save time by crossing it out rather than trying to erase it. Erased or crossed-out work will not be graded. No credit wen for am shown on the green insert. © Show all your work. Indicate clearly the methods you use because you will be graded on che correctness of your methods as well as the accuracy of your final answers. Correct answers without supporting work may not receive credit. CCopyrighe © 1997 by Eduction Testing Service and College Entanct Examination Board. Al sighs reservedSTATISTICS SECTION II Part A Questions 1-5 Spend about 65 minutes on this part of the exam, Percent of Section I grade—75 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. AGE DATA Age | 1900 | 2000 3 | 0.121 | 0.066 15 | 0344 | 0.209 25 | 0540 ] 0.348 35 | 0.700 | 0.480 45 | 0.822 | 0.643 55 | 0.906 | 0.781 65_| 0959 | 0.870 1. The table of data above provides the cumulative proportions for the United States population at selected ages for the years 1900 and 2000 (projected). For example, 0.344 or 34.4 percent of the popu- lation was at or under age 15 in 1900, while only 0.209 or 20.9 percent will be at or under age 15 in the year 2000. The graph below shows the cumulative proportions plotted against age for the years 1900 and 2000 (projected). The data and graph are to be used to compare the age distribution for the year 1900 with the projected age distribution for the year 2000. 1.0 Year 1900) © © & Cumulative Proportion © e & Age 40Ema (a) Approximate the median age for each distribution (b) Approximate the interquartile range for each distribution, (©) Using the results from parts (a) and (b), write a sentence or two for a history textbook comparing the age distributions for the years 1900 and 2000. 41 |2. A new type of fish food has become available for salmon raised on fish farms. Your task is to design an experiment to compare the weight gain of salmon raised over a six-month period on the new and the old types of food. The salmon you will use for this experiment have already been randomly placed in eight large tanks in a room that has a considerable temperature gradient. Specifically, tanks on the north side of the room tend to be much colder than those on the south side. The arrangement of tanks is shown on the diagram below. Window por Window —_—— North Describe a design for this experiment that takes account of the temperature gradient BOUL a aia 42eae ESP 3. A laboratory test for the detection of a certain disease gives a positive result 5 percent of the time for people who do not have the disease. The test gives a negative result 0.3 percent of the time for people who have the disease. Large-scale studies have shown that the disease occurs in about 2 percent of the population. (a) What is the probability that a person selected at random would test positive for this disease? Show your work. (b) What is the probability that a person selected at random who tests positive for the disease does not have the disease? Show your work, Oa aaa 434, A random sample of 415 potential voters was interviewed 3 weeks before the start of a state-wide campaign for governor; 223 of the 415 said they favored the new candidate over the incumbent. However, the new candidate made several unfortunate remarks one week before the election. Subse- quently, 2 new random sample of 630 potential voters showed that 317 voters favored the new candi- date. Do these data support the conclusion that there was e decrease in voter support for the new candidate after the unfortunate remarks were made? Give appropriate statistical evidence to support your answer.5. A company bakes computer chips in two ovens, oven A and oven B. The chips are randomly assigned to an oven and hundreds of chips are baked each hour. The percentage of defective chips coming from these ovens for each hour of production throughout a day is shown below. Percentage of Defective Chips The percentage of defective chips produced each hour by oven A has a mean of 33.56 and a standard deviation of 5.20. The percentage of defective chips produced each hour by oven B has a mean of 32.44 and a standard deviation of 3.78. The hourly differences in percentages for oven A minus oven B have a mean of 1.11 and a standard deviation of 4.28. Does there appear to be a difference between oven A and oven B with respect to the mean percentages of defective chips produced? Give appropriate statistical evidence to support your answer. 45EEQIF,..< STATISTICS SECTION IL Part B Question 6 Spend about 25 minutes on this part of the exam. Percent of Section I grade—25 6. You are planning to self a used 1988 automobile and want to establish an asking price that is competi- tive with that of other cars of the same make and model that are on the market, A review of newspaper advertisements for used cars yields the following data for 12 different cars of this make and model. You ‘want to fit a Teast squares regression model to these data for use as a model in establishing the asking price for your car. { | ] | | ae 1990 | 1991 | 1992 ] 1987 | 1993 | 1991 | 1993 | 1985 | 1984 | 1982 | 1986 | 1979 Asking Price Gn thousands | 6.0 | 7.7 | 88 | 34] 98 | 84) 89 | 15 | 16 | 14 | 20] 10 of dollars) The computer printouts for three different linear regression models are shown below. Model I fits the asking price as a funetion of the production year, Model 2 fits the natural logarithm of the asking price as a function of the production year, and Model 3 fits the square root of the asking price as a function of the production year. Each printout also includes a plot of the residuals from the linear mode! versus the fitted values, as well as additional descriptive data produced from the feast squares procedure. Model 1. 10.0 a ast, 0.0 a ee aeg2 ee oo 28 50 7.5 FS ‘The regression equation is Analysis of Variance Price = -58,1 + 0.719 Year soURcE DF SS_wS. Foo Predictor coef stdev trratio Regression 1 121.10 121.20 76.88 0.000 Constant -58.050 7.205 -8.06 0.000 Error 10 15.75 1.58 Year 0.71900 0.08200 © 8.770.000 «total ai 136-88, 251.255 Resq = 88.58 (eeModel 2 0.00 * 12 “ “ * -9.40 * oof coe oa0 6.60 Tea 80 the regression equation is analysis of Variance Mapcled eth P SHE Har Predictor coef seday cratic p soct OF ss skp Ceeatsne” STifeza PGES AF o.Boo —Regreecion T 5.8550 8.0890 17.77 0 B00 Sears" Gls$63 o.bids2 “35:30 $1000 Befee***°" lo BIMERE. 818432 220.2130 Rags 94.68 Bel oi bce Model 3 nae oso - : —s _ an : 0.09 » im Pare) . “0.30 80 aa a8 92 Year 0.60 2.20 1.80 2.40 3.007 the regrestion equation 1a anaiysis of variance SoeoTSEL ITS PT eat. Predictor cost tomate p somes or 88s kw ccratcee® SiSfua SST35'° 0 Boo Reoretsion 7.2 7.2 udm o.boo SEE GR bbe abled 05888 fevserston doar duoedd 5s = 0.2520 Resq = 91.9% ‘Total a 7.8572 aoESE. (a) Use Mode! ? to establish an asking price for your 1988 automobile. (b) Use Model 2 to establish an asking price for your 1988 automobile. ()_ Use Model 3 to establish an asking price for your 1988 automobile. 49(d) Describe any shortcomings you see in these three models. (@) Use some or all of the given data to find a better method for establishing an asking price for your 1988 automobile. Explain why your method is better. 50EXDIF...c If you need more room for your work, use the space below END OF EXAMINATION 51Ga Answers to the 1997 AP Statistics Examination Multiple Choice Section I: Multiple Choice Section Blank Answer Sheet Listed below are the correct answers co the multiple- @ Section IT: Free Response choice questions and the percentage of AP candidates 1 Student Preparation for the Exam who answered each question correctly. A copy of the Free-Response Questions, Scoring Guidelines, blank answer sheet appears on the following pages for and Sample Student Responses reference. ® Section II, Part A Section II, Part B Section | Answer Key and Percent Answering Correctly tem Correct Percent Item = Crrect. Percent tom Correct Percent, oer COMmcu mets (oem) 1 E 866 5 B 739% 2 c 650% . D 81% 4 D 73% 6 c 55% 3 cl 759% 6 B 83% 2 E 520% 4 D 93% 16 E 69% 28 B 55% 5 A 73% v B 748% 29 A 60% 6 A 680% 18 E 63% 30, A 4696 ie B 61% 19 E 91% 31 A 3% 5 B 80% 20 c 36% 32 D 2% 9 D 80% 2 B 69% 33 c 309% 10 8 87% i A 56% 34 A 53% 1 B 749% 2 A 68% 35 6 6580 R D 76% Et B 70%e e e e ys 1 besa soon openatate isons 20! S100 on Stag guages ey no a0 ee C0088 86 0} 0 sensei un ptg vrmmees emis se aes PHD see) ema ones | tom Sooroueycouees = 310.0 is ooioisd 8/8 8 maa shia 9/08 ‘oon 2 sd 8/9 8 Banh fe 9/8 8 sna dent ‘som sououoo3 ) vo ale 8 oasnnae3 /0.6 8/0 8 ayo sioo® . 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(DO NOT PUT RESPONSES TO EXAM QUESTIONS IN THIS SECTION.) BE SURE EACH IAAK IS DARK AND COMPLETELY FILLS THE OVAL. 1®@OOO 4DOQOOO 2DOOO® sDOOO® 23@DOO® | Bo Nor COMPLETE THIS SECTION UNLESS INSTRUCTED TO DO SO, R. this answer sheet is forthe French Language, French Literatura, German Language, Spanish Language, of Spanish Literature Examination, please answer the folowing questions. (Your responses wil not afect your grade) 41, Have you vd or studied for one month oF mere ina county where the language ofthe exam you are now taking is spoken? O ws No 2, Do you ragulary speak or hear the language at hme? Ow Ono INDICATE YOUR ANSWERS TO THE EXAM QUESTIONS IN THIS SECTION. IF A QUESTION HAS ONLY FOUR ANSWER. OPTIONS, DO NOT MARK OPTION (E). YOUR ANSWER SHEET WILL BE SCORED BY MACHINE. USE ONLY NO. 2 PENCILS TO MARK YOUR ANSWERS ON PAGES 2 AND 9 (ONE RESPONSE PER QUESTION), AFTER YOU HAVE DETERMINED YOUR RESPONSE, SE SURE TO COMPLETELY FILL INTHE OVAL CORRESPONDING TO THE NUMBER OF THE QUESTION YOU ARE ANSWERING. STRAY MARKS AND SMUDGES COULD BE READ AS ANSWERS, SO ERASE (CAREFULLY AND COMPLETELY. ANY IMPROPER GRIDDING MAY AFFECTYOUR GRADE. 1®@OOO 2OOOOD 31 @®OOOG 2BOQOGO 7 @OOOOG 2 @ODOO® 3@BOOOO z2@aOOOS 83 O2®OOG 4@QOOO 2DOOO® ROR ORCRORG! 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However, for inference problems the rubrics required students to explain the method used along with the assumptions for the method, and to look carefully at the data to see if they thought the assumptions were satisfied. The analysis had to be followed by a clearly scated correct conclusion, written in che context of the original question. ‘Many students had difficulty determining whac method to use, often trying two or three approaches or mixing approaches in ways that were unclear to the faculty consultants at the Reading. In addition, students had difficulty explaining assumptions and rarely looked at the data to see if assumprions were satisfied. Conclusions were often poorly written both in terms of the statistical concepts and the grammar, Students must learn to view statistical inference as a process that involves five steps: Dv 2) 3) understanding the problem to be solved, finding an appropriate method, checking the assumptions for the method against all the available data, 4) 5) carrying out the analysis, and vwriting a clear and correct conclusion in the context of the original problem, Student preparation on the basic principles of blocking and randomization for designed studies was also quite weak. For question 2, on the design ofan experiment, many students appeared to be confused about whas constituted the treatments and what consticuted che experimental units, Among those who seemed to grasp this idea, many did not understand that blocking is dhe best way to reduce variation among the experimental units oF got confused about how to block appropriately. In addition, many did not under- stand hac randomization is necessary to reduce bias and to allow probability-based methods of analysis to be used after the data are collected In summary, the examination contained a fairly easy. multiple-choice section and a challenging free-response section. The questions in the larcer appeared to be fait in light of the Course Description, bur many students were not adequately prepared to explain and defend methods used and to verite clear conclusions reflecting both good statistics and good writing. Free-Response Questions, Scoring Guidelines, and Sample Student Responses ‘The answers presented here are actual student responses to the six free-response questions on the 1997 AP Statistics Examination. The scudencs gave permission to have their work reproduced at the time they took the exam. These responses were read and scored by the leaders and faculty consultants assigned to each particular question and were used as sample responses for the training of faculty consultants during the AP Reading in June 1997. The actual scores that these students received, as well asa brief explanation of why, are indicated. 57Question 1 Scoring Guidelines 4 Complete Response Correctly uses the graph or (informally) interpolates in the table co approximate the medians and quartiles. The numerical values must make practical sense within the context of the problem. Approximates medians for 1900 to be about 23 or 24 and for 2000 about 35 or 36. Approximates the interquartile ranges for 1900 to be about 40 - 12 = 28 and for 2000 about 54 - 18 = 36. May not caleulate the IQR but gives a clear indication in che writing that che distance berween the quartiles is a measure of spread. States clearly that the U.S. age distribution will shift toward larger values for 2000 as compared to 1900, wich greater variability in 2000. The statement is consistent with the numerical results from parts (a) and. (b) and is written in such a way that it would be understood by the general population. Sample 1 3 Substantial Response Approximates medians and interquartile ranges neatly correctly from the graph or the table. Need not calculate the IQR if there is some indication that the quartiles can measure variability. States clearly that the U.S. age distribution will shift toward larger values for 2000 as compared ro 1900, but ‘may not specifically mention the increase in variabilcy 2 Developing Response Gives a poor approximation for the medians or interquartile ranges, but seems to have some understanding of what these measures represent. Or, provides at lease a weak but correct statement on. the nature of the changing populations. 1 Minimal Response Indicates some understanding of at least one of the three parts of the question. (2) Approximate the median age for each distribution. (408 [59 £ wchin age £25 melian oge AZ Z2T yrs 2000 ay 2 wcdan gee ee we age BE yesSample 1 (cont.) (b) Approximate the interquartile range for each distribution. 1100 teoo = 2s ee wes 16 2x2 53 Evshe s wu ex £ 34 3q-\e Zaye) ws) sxe: Faye)" ** ——— > mca) velue S (©). Using the results from parts (a) and (b), write a sentence or two for a history textbook comparing the age distributions for the years 1900 and 2000. At the turn of te conta, in (400, *he og of pecrt= was wach lower then if all b. qhen we Wit te year 2000. Tn laoo ieee medion age wae aly 22 3. 2b yous old Ale 2000 ik will be about 36- Rope now, The widdle SOT SF pope ol in the year oe Laving leage: w 0D vere ekueen Wed 39 91 whe $.2000 the midlle so% Ul be between 18 omk 59 genre old, Commentary: ‘The medians and interquartile ranges are clearly specified for both the 1900 and 2000 data. The student describes the shift toward an older population in 2000 by stating how the median increases and how the spread af the middle 50% also increases. Score = 4 59Sample 2 (a) Approximate the median age for each distribution. The median age te eth dite baben ald gop of he ge whore th Oh “tpl toa wat oA a below foe! 7) Ae cad (Wl we Ye J cdo grt Chie 6 ib ys. th ape, wh S194 the papulldben, a1 Gn as tabobahrs he aggre kes eae Gn Ag tbe hh Hots tabblo spo m eds bly pboe Byes, ci Ul At fe Pople A «7 kl 4g FIs (b) Approximate the interquartile range for each distribution. Th vbeywer dl pipe 6 9 pital b te ee eg sue Oe a tle HW wck pypiftin ds Ghibey. Th? Cap fad by shba dh hg (gp tgget) bo haw Fhe igpar) 26 %> ]dyr™ 5 eafeaed W- oe ed- te =. Pos - ays * Bhs: Son: \ yw: ope Bo He SS yr - Wyre PG "0 Th apr’. "08 de 200 Ub yn, whl ber SOQ I 3 yn, (©) Using the results from parts (a) and (b), write.a sentence or-two for a history textbook comparing the age distributions for the years 1900 and 2000. 4h te yee Gite popilot, ox o while apt be thle, flit bas Z te Yor "Glan ee ia +K, ‘pin ig vill thy 4 to Abitord as 73 cemecitate bw? ibs, /» 100 MO), Nhe Ge P Me igs att be po Puce wally the A Ae ply YZ, Commentary: ‘The thinking of this student is clearly stared in words; the reasoning on both the medians and the interquartile ranges is correct. The conclusion concisely states how both the center and spread of the ages increase between 1900 and 2000. Score = 4 60Sample 3 (@) Approximate the median age for each distribution. The median as® for the population of 1400 lies betwee! the ages of IS and GS, whee 50% of the apulatiot rs abeuc a& below the median. This age is contained 1A (8,8), roughly 23. The niredian age €or the G.Goo (ep «leben ies betweer ~+he ages of BE and 45, rownly ~ 37. (>) Approximate the interquartile range for each distribution. The TAR is Q,7@;), For 'f00, a, 37 and Q, X10. There fore , the FAR eR? years er O00, Q,% 63 and Q,* 17. There fre, the DQR % 36 years (© Using the results fromm parts (a) and (b), write a sentence or two for a history textbook comparing the age distributions for the years 1900 and 2000. During The year 1900, the majority of the U.S. gopubtion ranged Com the eases of [0 237, whrle 14 the year Boece, the populate] ranged Lreni (7 te 53 yrers of, En gerere| fhe age of the “averse ~ Ee ic hee eee ee Fre MaSically, Commentary: Correct reasoning and good approximations are provided for both che medians and the interquartile ranges, Although the conclusion states that ages are increasing, the use of interquartile ranges to express this idea is a bit confused. Both the “majority” and “population ranged” terms-are not quite correct. Score = 3. aisQuestion 2 Scoring Guidelines 4 Complete Response Shows four blocks of two tanks each, with the pairs of tanks being in nearly identical conditions with regard to temperature. The blocks are (1,4), (2.3), (5,8), and (6,7). Scates cleaely chat this isthe potentially most effective arrangement of blocks since these paits should be the most homogencous. Explains a correct method for randomly assigning treatments to blocks. 3 Substantial Response Shows ewo blocks of four tanks each which take into account the north-south temperature gradient. The blocks are (1,2,3,4) and (5,6,7,8). Or, shows four blocks of two tanks each which take into account the north-south temperature gradient. These blocks are (1,2), (3,4), (5,6), and (7.8). Os shows a correct design for the case in which both foods could be used in each tank. Sample 1 Explains a method of randomly assigning the wo treatments to tanks that shows some understanding of randomization. 2 Developing Response ‘Shows a design that correctly takes temperature into account, but ignores the randomization, Or, explains a method of randomly assigning the wo treatments to tanks and indicates that cemperacure is o be taken into account in the analysis, 1 Minimal Response Shows some knowledge of what is meant by blocks, but is not cleat on any sationale for choosing blocks or any method of assigning treatments. (Or, states chat che ewo treatments must be randomly assigned co tanks but ignores the temperature gradient 2. A new type of fish food has become availabie for salmon raised on fish farms. Your task is to design an experiment to compare the weight gain of salmon raised over a six-month period on the new and the ld types of food. The salmon you will use for this experiment have already been randomly placed in eight large tanks in a room that has a considerable temperature gradient. Specifically, tanks on the north side of the room tend to be much colder than those on the south side. The arrangement of tanks is shown on the diagram below. Window pote ‘Window 62Sample 1 (cont.) Describe a design for this experiment that takes account of the temperature gradient. Because of te coon’d symmetry, Vk is) possible te meteh each tenk with another thet should have very semiler, Fonot egusl temperatures, The matchings ore 4 2,3 3, ¥ and ©, F, From each peir, choose one teak te be fed cite the new ford and one Henk te be fed orth He old feod, This choice sheald be dene rendomly Gussibly by the tas of « coin), AL both the heginniny ant end of the sie week period, find meen weight of He Fish an each type of food, Then caleulate dre difference dm weight gh gee end dehemire 3 wid is orgn ificanh Commentary: ‘The idea of pairing similar tanks to form homogeneous blocks is clearly stated, as is the notion of randomly assigning treatments to the tanks within a block. It is not necessary 10 discuss the analysis ofthe resulting data jn any detail. Score = 4Sample 2 2. A new type of fish food has become available for salmon raised on fish farms. Your task is to design an experiment to compare the weight gain of salmon raised over a six-month period on the new and the old types of food. The salmon you will use for this experiment have already been randomly placed in eight large tanks in a room that has a considerable temperature gradient. Specifically, tanks on the north side of the room tend to be much colder than those on the south side. The arrangement of tanks is shown on the diagram below. ‘Window poe Window Describe a design for this experiment that takes account of the temperature gradient. To account Sor the temp, gradient, He salmon Should be divided into He Blowing groups: in the 1rd : i, weeld be Bach Cish in these ‘P eae relatively Sane temp. environ erth aS + t+7 Ofer fish In tHe gp) lased on room locaton, ald New rendomly{assign | Fish in eee gine the new foc, es gis re other Frok He ad fay. phter 6 months, compare te weight 92’ oF cach Sisk In cach group. Pry aay auger ae) in the weigh * gein weeld pare +o feo " . Yo tae news Sood, since femperotare Ci tas i have peen neutralized, Commentary: In this response, the block arrangement for tanks is chosen correctly and randomization is used properly. The conclusion is a clear statement on the purpose of blocking and randomization, showing that the student understands the basic principle. Score = 4 64aL oh We vont Start arta 9 Sample 3 rp ‘A new type of fish food has become available for salmon raised on fish farms. Your task is to design ‘an experiment to compare the weight gain of salmon raised over a six-month period on the new and the old types of food. The salmon you will use for this experiment have already been randomly placed in ight large tanks in a room that has a considerable temperature gradient. Specifically, tanks on the north side of the room tend to be much colder than those on the south side. The arrangement of tanks is shown on the diagram below. ‘Window Door Window North Describe a design for this experiment that takes account of the temperature gradient. The room wourtd we dividé WhO tpo Decits. Tay Wlock youd VE ob tants 1,2,3,and4 on Ye morn sidt Qf The + oo" Tr otter wowd WR ahtwiks 56,2 andl Mw s volt TONS tanh 4, Pr where p, denotes the proportion of voters favoring che new candidate before the incident and p, denotes che proportion of voters favoring the new candidate after the incident. 4 223 4 _317 = 2232537, == Pe 415 P30 Both samples are large enough that the normal distribution approximation is appropriace. Hy: Py = Py 503 537-503 ss bof SOT 8. Ba- BE my POI SINGS Gq) 2 = 1.08, approximately. prvalue = 1 ~.8599 = .14 While the proportion of voters in the sample supporting the candidate after the unfortunate remarks were maide is less chan the proportion of voters supporting the candidate before the remarks were made, the difference is not significant and can reasonably be antibuted to chance, aeSample 1 4. A random sample of 415 potential voters was interviewed before the start of a state-wide campaign fr poveraor 223 of te 415 sid hey fred the ew candidate oer ie incumbent ade several unfortunate remarks. the election. Subse- eth neermic sample of 630 potential voters Showed that 317 vers favored the nw cand Do these data support the conclusion that there was a decrease in voter support for the new candidate after the unfortunate remarks were made? Give appropriate statistical evidence to support your answer. LMeckion, Birce O shave use Mompde peopeciiory, Leach chaueation usithin gach Aemple ans Andupendent 4 amd mip 41 (I-p,), Naps axel ra (i-ba) ante ado geeahae than or 2gua-l to ) Burd yaa o too propsction Zee. La found He Ateendaced Qe Rte He peepentin to be Srp 2 jee , Pall-pe) 2 OMNSS TAB aunerthe Da ae and Aan beneguad ee , Hoag Compu fhe GRiticot z-velue peat a which, thule /:08/7,Sample 1 (cont.) The p : ty Hat 2 ta ysalie than /. ott 4a +139. There he mat Undigh. Mgrupiccnt aviderce to eh ot He 5, D8 The mou Candida chum, Rornasebo did ey Commentary: The student writes out in great detail exactly what the reasoning process is. The reasoning is very clear and easy to follow. Ir cavers the nature of the problem, the assumptions, the mechanics of the test, and the conclusion, which is stared in the context of the problem, Score = 4 72Sample 2 4. A random sample of 415 potential voters was interviewed 3 weeks before the start of a state-wide campaign for governor; 223 of the 415 said they favored the new candidate over the incumbest. However, the new candidate made several unfortunate remarks one week before the election, Subse- quently, a new random sample of 630 potential voters showed that 317 voters favored the new candi- due N=4IS X= aad Ng=G3Ro %473\4 Do these data support the conclusion that there was a decrease in voter support for the new candidate afer the unfortunate Fermarks were made? Give appropriate statistical evidence to support your answer. yer POV Hot Piz Py WR Gees Berne eh Pa Proportion of vorer Spot 3 Hat py? Pa \ Week be fore be ction Q praparhon Z +St + Z= 1.083 prval= .\397F Canclosion + do not reyect X2= 2F Ho because p-al= 1ST Aas Gag \oefere (S rot Stanshcall Pas .sosa) clearer SIQME Cantar fe «10 5 a > USiile there 1S some. S- eviderce Gost Boy Taser tree is Wa aA evidence tO crc sect to See ted 1 fro there. was adecrase SLR Gas a pe WANGer SUpport far He Zz est t Ness candidote ater 7 tne Unforrumde Yermarrs, NPL? S PABC-SHD= wer vrowe | s 2A2-FBs WCrpyI7S = ASC -4.69D= 194,085 Pars > 620CSoAD= 317F.GarS MO p75 > Asa975 mest likely tno State nos 7 1 x SORNAE Site Commentary: The response cleatly covers the type of rest being done. the assumptions (with a small ertor in notation), the rest statistic and p-value, and the correct conclusion. The conclusion provides a statement in the context of the problem. Score = 4Sample 3 4, & random sample of 415 potential voters was interviewed 3 weeks before the start of a state-wide ‘campaign for governor, 223 of the 415 said they favored the new candidate over the incumbent. However, the new candidate made several unfortunate remarks one week before the election. Subse- quently, a new random sample of 630 potential voters showed that 317 voters favored the new candi- date. Do these data support the conclusion that there was a decrease in votet support for the new candidate after the unfortunate remarks were made? Give appropriate statistical evidence to support your answer. Hier Trete wes 92- change in vetee be? Suppers qedecmset after te remarks Wa There was a decrease in velee Pap>o soppeer after the ‘remarks a =O te SR7y cae fhe 608%" Ge at-Py + Pal Pa) Wy ey Zz: \,O7 P= 1422 Ke Of Based on Flack Lk sutiicrenr evidence, fa i fe eject Be the there? was no change in voter Soppork s%tae jhe remarks the new - candidate nade. Commentary: ‘The student carries out the correct test and makes a proper conclusion, bus some of the symbols are not defined and no mention is made of assumptions. Score = 3Question 5 Scoring Guidelines 4 Complete Response A. Selects an appropriate test of significance. Observes that data are paired by hour of day and indicates a paired t-test is appropriate OR observes that the data are paired by hour of day and justifies choosing a two-sample t-test (or confidence interval for the difference of two proportions) OR worries about assumptions for a t-test and so chooses a sign test OR performs a substantial data analysis. B, States and addresses assumptions necessary for t-test. ‘The dot plot below shows no evidence that the differences aren't normally distributed. 25 50 75 (For 2 ewo-sample t-test, mentions thac outliers indicate a potential problem.) C. Carries out a test of significance. States the hypotheses correctly, with two-sided alternative, defining any nonstandard symbols. Hy? ny = Byrn, = 0 Hin, # worm, #0 Calculates an appropriate test statistic, possibly ‘with trivial arithmetic error. d-0_ il pene Sifq | 428/09 =078 (Por ewo-sample t-test, t = 0.519 and p = 0.61, pooled or unpooled. For a sign test, +-+-++-0+ s0 P= 0.727.) Correctly approximates the P-value from a table or calculator. Wich 8 degrees of freedom, the two-sided P-value is 0.46 (OR compares t= 0.78 with critical value of 2.306). OR constructs and interprets a 95% confidence interval for the mean difference: 14(2. 316( 438) 113.29 or(-2.18,4.40) a OR a 95% confidence interval for the differ- ence of two means: (-3.47, 5.69) D. Correctly states a conclusion in the context of the situation. ‘The difference in the mean percentages in the samples of defective chips produced by ovens A and B isnt statistically significant. [there was no difference in the percentages, a mean absolute difference of 1.1] or greater would happen 46% of the time with random samples of size 9. Os for the confidence interval: Since the confi- dence interval includes zero, there is no evidence that one oven differs from the other in terms of mean percentage of defective chips 3 Substantial Response Performs a test of significance but Doesn't mention the assumptions for the rest used. OR States an incorrect conclusion OR Males ewo or theee less significant omissions or errors in the test of significance, such as doesn't make it clear by words or formula which test they are using chooses a ewo-sample eestor a sign test without considering che paired terest fails co lise hypotheses does a one-tailed test or forgets to double the P-value ‘says must use a t-test because n is small uses 2-test, nor Cxest mentions normality assumption but doesnt check ie graphically or appeal co robustness confuses parameters and statistics 1 docsnit define nonstandard symbolsQuestion 5 Scoring Guidelines (cont.) 1 Minimal Response forgets “77 in formula fore Recognizes thar the problem involves an inferential statistical argument 1 uses wrong critical value or degrees of freedom Does little more than carry out the mechanics of a test 15 “acces” he nll hypothesis or uses similar caress ra cuch as those done by a caleulaton language in conclusion gives correct, but minimal, conclusion (“do not ‘Note: Since we are using holistic grading, a deficiency reject H,”) or a generic conclusion that doesn't in one part can be compensated for by outstanding relate to the ovens work in another. 2 Developing Response Performs test of significance except makes both major errors OR an equivalenc combination of errors. Sample 1 5S. A company bakes computer chips in two ovens, oven A and oven B. The chips are randomly assigned to an oven and hundreds of chips are baked each hour. The percentage of defective chips coming from these ovens for each hour of production throughout a day is shown below. Percentage of Defective Chips Hour | Oven A Oven B 1 45 36 2 32 37 3 34 33 4 31 34 $ 35 33 6 37 32 7 31 33 8g 30 30 2 27 24 “The percentage of defective chips produced each hour by oven A has a mean of 33.56 and a standard deviation of 5.20. The percentage of defective chips produced each hour by oven B has a mean of 32.44 and a standard deviation of 3.78. The hourly differences in percentages for oven A minus oven B have a mean of 1.1] and a standard deviation of 4.28. Does there appear to be a difference between oven A and oven B with respect to the mean percentages of defective chips produced? Give appropriate statistical evidence to eae pov etn. Te test for, a dMerence cen oven d cel mote am an 2 ena we 7 gee des: awl be esol The reasen *s a . beaLler phe LZ shows a deed peshre a4 soci Lon bedwren the Percentage of defleckive chips. The prota bittySample 1 (cont.) of obfaing such a Ag A Nneavity is b-hoves Reording to @ Minene Fegression Hot TH ae ndente < wists, a tee saeple ttesl fanned, bs, fen 4 Lee = pemsin ef 6d This, the nlf hyper bases 7 lV EL ices of fhe peceeol, debe Or 'PS Vs . The olfecna hey, L . not thod He tnean bhacorce YOUPhes 73) CO. A thendard aloha oh. 62 6D Goel, The general €¢ ution fs a one gample £ yest upon the diklerence ov 4 4a Vr The degrees of Kee Jam (sea ce Subshhting 4s SE or Hz 7790 The pre bab, SrA of of oblarnrng guch a telatHishe ef 2 pile. 776 Oarce O deg.ees oh freedom ys , USER Thrs peebaby (ty value 13 greats Phan ak he The wyll/ hyae thesis ) 7? / tferen ce eels between vm 4 pnd Oren @ for the poeportion of defective tee. must be acces ec. Commentary: ‘The response provides a detailed explanation of why the data are regarded as paired (although the regression part is not essential) and even plots the data. The paired t-test is carried out and a correct conclusion is stated in terms of a comparison between the ewo ovens. (It would be good to plot the differences to show that there are no outliers.) Score = 4 77Sample 2 5. A company bakes computer chips in two ovens, oven A and oven B. The chips are randomly assigned to an oven and hundreds of chips are baked each hour. The percentage of defective chips coming from these ovens for each hour of production throughout a day is shown below. Percentage of Defective Chips Hour | Oven A Oven B 1 45 36 2 32 37 3 34 33 4 3h 34 5 35 33 6 37 32 7 31 33 8 30 30 9 27 24 ‘The percentage of defective chips produced each hour by oven A has a mean of 33.56 and a standard deviation of 5.20. The percentage of defective chips produced each hour by oven B has a mean of 32.44 and a standard deviation of 3.78. The hourly differences in percentages for oven A minus oven B have a mean of 1.11 and a standard deviation of 4.28, Does there appear to be a difference between oven A and oven B with respect to the mean percentages of defective chips produced? Give appropriate statistical evidence to support your answer. _ Te dota is given tous in matched Paits form, protche hoor. “To analyze Mathes pairs data TAwill use a one ~Somple Attest On The dickerees Lge bis to Aqwount Sor the non - indapadere thet matched ers has. He MeO Hy MieetO Kyac> AM THe — WNHO _ 77g S4OF Fe TEI Wg n=q Tin TE AS (05 de=g 72Sample 2 (cont.) crital tye gg 2308 3, 3067.7 76 Beause the wit Ff less. then “ ++ statistic L connet rejeet Ho infqvor oF Me. That ne evidee to sa est vu dittereny in the percentage oF bared ates Ve av in the oven, “Commentary: ‘The student correctly recognizes this as a matched pairs problem and analyzes the data accordingly. “The conclusion is correctly stared in context. Although assumptions are nor mentioned, the student did look ac che differences, as indicated by the numbers added to the chart. Score = 4 [79Sample 3 . A company bakes computer chips in two ovens, oven A and oven B. The chips are randomly assigned to an oven and hundreds of chips are baked each hour. The percentage of defective chips coming from these ovens for each hour of production throughout a day is shown below. Percentage of Defective Chips Hour | Oven A Oven B 1 45 36 2 32 37 3 34 33 4 31 34 5 35 33 6 37 32 7 31 33 8 30 30 9 27 24 “The percentage of defective chips produced each hour by oven A has a mean of 33.56 and a standard deviation of 5.20. The percentage of defective chips produced each hour by oven B has a mean of 32.44 and a standard deviation of 3.78. The hourly differences in percentages for oven A minus oven B hhave a mean of 1.11 and a standard deviation of 4.28. Does there appear to be a difference between oven A and oven B with respect to the mean percentages of defective chips produced? Give appropriate statistical evidence to support your answer. See student response on facing page. 80Sample 3 (cont.) an 748 Ae pucenTge. depsBiuze Chipt« gor ‘Aa A4p Abc preening 2 obpetnie Chips gor Ae Hib -32-44 ae q % Bb 2.0092 & CohusLick fom 7) -B2 2 6090S (from T1-B2. wth, df ly Aces Car om OD neat hers. ae ut smog iviglnce to iycet He Aw favor Of Hoe rar for Bins 20 n0 klwen the prcentagt @ chyecliir chip bitin evens A aref & Rash. cto even Ate akowek cht ad wie Ang Laas Hm 16 Lt my aptect Ep Sereee en ae eae arr rae % Anyis sorte tek ae Commentary: Here, the data are analyzed by a two-sample t-test on the difference between two means. Given the assumption ‘of two independent samples, the analysis and conclusion are correct. The student correctly notes that there is some skewness in the data. Score = 3 81Question 6 (Investigative Task) Scoring Guidelines 4 Complete Response L I. ML NV. Correctly estimates the asking price in dollars for at least ewo of the three models, including back transforming the predicted value for at least one of models b oF c. a. Price = -58.1 + 0.719(88) = 5.172 asking price is $5,172 b. Ln(price} = -14.9 + 0.185(88) = exp(1.38) = 39749 asking price = $3,975 c. Sqri(price) = -13.3 + 0.176(88) = 2.188 (2.188)? = 4.7873 asking price = $4,787 380 Describes the major shortcoming to be the non- linear pattern in the seatterploc oF residual plot for all three models. Suggests a new model that successully deals with the non-linearity of the data. The prime contenders for this model are: Fica simple linear model after the first two or three years are dropped. (2 =.978 with liccle pattern in the residuals after dropping 79, 82 and $4.) Fit separate linear models to the earlier andl later years (R? = .985 for the years 86 to 93, with little pattern in the residuals.) Fica model that attempts to model the curvature in the data, For example, fita quadratic model to all of the dacs (R? = 974 with litle pattern in the residuals for a quadratic model.) Justifies why this model is bettes. For example, comments that there is no pattern in the residuals as seen from looking at the fitted model on the scatterplot or from looking at the residual plot. ae 3 Substantial Response Fails to do one of the following satisfactorily: Pare (for example, by filing to back transform the prediction) describe the major shortcomings of the three models 1 justify why the new model is better (for example, by failing to comment on the residual plor) 2 Developing Response Fails to do one of the following satisfactorily: Pare I and describe the major shortcomings of the three models Parc and justify why the new model is better suggest a new model and justify ic describe the major shortcomings of the three models and justify why the new model is better. 1 Minimal Response Gives correct responses to one of the items I, Il, of HL above. Note: Students cannot get IV correct without first specifying a new model.Sample 1 (@) Use Model 1 to establish an asking price for your 1988 automobile. Price = 58.1 40.119 (88) = [e5.s70\ (b) Use Model 2 to establish an asking price for your 1988 automobile. Qu Price = —14.9 + 0.185 (88) = 1.38 vier = @' FF 2153, 970 (©) Use Model 3 to establish an asking price for your 1988 automobile. SPriea = 13.3 + OAT (8B) = 2.198 Crier = 2.188% ~)94, 790Sample 1 (cont.) (@) Describe any shortcomings you se in these tzee models Aitleagh the couvelation coefficients ave af quite large, tle veridual glob alk show a dinkined potun, wliclh wear that witlen Gt is tle covet one fev tle date (©) Use some or all of the given data to find a better method for establishing an asking price for your 1988 automobile. Explain why your method is better. Fvow te plet Neodel 4 ck do fear tut a bctln fit for te Anta vtertdh Cy. tro Lies iuokead of ace. the fivet cue woutd be the beast-aquerer veqvecsion Line on te yearo prioy ke 1966 and would Ge valid fer there yeave, WEL the otter exe wold & the vequersion Live on tle > of 1986 and bakes, ond would Ke oatid CO yenvo Fa thin case, amy pativn in the veridual plot vot dian ppeaw, and the aabing prsee of the 4933 arbousi con be dled fren the weeond Live of ae Ke. oar od tine Ant Live Commentary: Parts (a), (b), and (c) show correct calculations and (d) contains a comment on the patretn in the residual plots. Pare (@) contains a clear description of how the data could be split into two groups, each showing a linear trend boc with different slopes. Score = 4 [84 |Sample 2 (a) Use Model 1 to establish an asking price for your 1988 automobile. erites ~ SEV NA yen? = -5B.) + 1WV4- $4 2 TATL Ghovsand dollere) c- Price Frain) (b) Use Model 2 to establish an asking price for your 1988 automobile. he price - (44 + NBS-yeor = “HAF 185-88 bp 7 |.o% pee s BATT Hoveond 8) fe prigee 429795 (©) Use Model 3 to establish an asking price for your 1988 automobile. peice = 713.3 + bear = -\3,3 ¥ N16 8S = V.\ 84 perce 2? \get= 4.197 (thovsand 3) proce 84197) 85Sample 2 (cont.) (© Describe any shortcomings you see in these three models. The veoduals, which should be voubow in the eck reqvesson, exhibi} curved acters ee avaphs- Aloo, #%, which ehovdd ve ok least 81 ov 4, 31 446 ow every qeephe or lower ( price Vs. Ds year does nok correct Ahig. ° ugeedtinersene fing a beer method fr exalising an asking pc fr your Eliminate Lrom our dghe pool all cars ore thaw three years away from ovr \V@F car® before \VWES or offer oe Ahen, We get a doka set wth the following araph (oketehed Svom colevleter): and 0 least eq veces Fey Vession erie| . of Cprice + -82 = Lone Geer). - yeow The plot gt the rodvals te Bo < which gs Leirly mundom- year Subshirvting tn oer year, we getia prec of prices - 42+ [,0%6ls9) = 444g = BUG which — Seems correspond to neorby years Laicly well Commentary: “The numerical calculations in the first three parts are correct. The pattern in the residuals is recognized, The solution to improve the fit is to concentrate on the years around 1988, and this is reasonable way co improve the fit. Score = 4 86Sample 3 (a) Use Model 1 to establish an asking price for your 1988 automobile. $(88)= FATD these dellers BANTD tres’ os -s%,1 10, 79+ 8 () Use Model 2 to establish an asking price for your 1988 automobile. = 1,38 af wool Pe 5 a 709 Heard dlees 14.9 + 0.18538 = (©) Use Model 3 to establish an asking price for your 1988 automobile. 2 “13.34 O.176- BE= BIBT 2,188 = 4787S theserd dillersSample 3 (cont.) (@) Describe any shortcomings you see in these three models. These models inchde all of the deta, According fo fhe regression egeshon for the First mudel, 0 1980 cor vould sell for -O.SE Howard dollars, We know , You can self almost ary that cors will sell for a minimum amouat of mo coe Gor about a thevsaad dellacs, You shevid there not include data fom cars older than a certain yes (©) Use some or all of the given data to find a better method for establishing an asking price for your 1988 automobile. Explain why your method is better. T+ oppenrs that the regression equation for this date woull Fit beter if the date From years (977 and 198) were omitted. Thue were to Find out prices for cors older than 1784 we would probably Sind that most of them sold for grand J fheaand dollars, by ontHing ~ Gor mete! L "Dt ad Gh oor new Cepression egetionis ~BII34A+ O.974 7-year, 7 £82 97,1R% This is & much beter Fit thaa the previous eg ration, Our new asking price would be 4, 64 thousand dellovs which would be Closer 4 the true market valve, Commentary: ‘The calculations in (a), (b), and (6) are correct, In part (e), a good solution is suggested in terms of eliminating the early years from the analysis. The main weakness of the response is that the pattern in the residuals is not recognized in (d). Score = 3 88 |Ga Statistical Information Table 4.1 — Section II Scores College Comparability Studies | How AP Grades are Determined Reminders for all Grade Repore @ Table 4.3 — Grade Distributions Recipiencs Table 4.4 — Section I Scores and & Reporting AP Grades AP Grades Purpose of AP Grades Table 4.1 —Section II Scores “These ate the score distribucions for the total group of candidates, on cach frce-response question from the 1997 exam. Pe Cm Ce Numberof At | Numberof — % At | Number of % At Score Students Score | Students Score | Students Score 5H 7 ist is 948 124 3 1261 165 124 16.1 179 23 a 2 iia or 4675 od i410: 185 1 1612 2b 885 ne 969 7 a 2797 366 530 69 3551 464 *NR 200 26 188 25 59 24. Cr Ca Number of Numberof — % At [Numberof — % At Score Students Students Score | Students Score Se 170 22 7 157 21 6 2a Br 5 292 38 a 159, 2 19 02 580 26 3 2629 344 1285 169 594 78 2 oo ie | ae 330) 1841 261 1 1128 148 1626 212 734 36 a0 2168 283 isis ie 2570 336 NR 148 19 38 45 467 6 “NR — No response. Suident gave either no response ora response not on the “Question 6 was read by wo different Faculty consultants and the ro scores were combiny Toual Candidaces role 7,686 1046 7.646 Mean 1.89 1.06 139 uaa Standued Deviation 0.84 139, 1.08, 2.05 Mean as % of 33 7 35 2 Maximum SeoteHow AP Grades are Determined AD Statistics students can receive 0 to 50 points in each section of the exam. However, these scores are not released to the student, school, or college. Instead, these raw scores are converted to grades on an AP 5-point scale, and it is these grades that are reported. This conversion involves a number of steps: 1. The multiple-choice score is calculated. To adjust for random guessing, a fraction of the number of ‘wrong answers is subtracted from the number of right answers. This fraction is 1/4 for five-choice questions (as on the Statistics exam), so that the expected score from random guessing will be zero. 2. The free-response score is calculated. When the face-response section includes two or more parts, those parts are weighted according to the value assigned to them by the Development Committee. This allows the Development Commitee co place more importance on certain skills to correspond to their emphasis in the corresponding college curriculum. 3. Acomposite score is calculated. Weighting also comes into play when looking at the multiple- choice section in comparison to the free-response section. In consultation with experts from the College Board and ETS, the Statistics committee decided that each section should contribute an equal amount to the total score. The maximum. composite score was 100, with each section 1g up to 50 points. The Scoring ‘Worksheet on the facing page details the process of converting section scores to composite scores for this examination. contrib —s 4, AP grades are calculated. The Chief Faculty ‘Consultant sets the four cut points that divide the composite scores into groups. A variety of informa- tion is available to help the CEC determine the score ranges into which the exam grades should fall: 1 Discributions of scares on each portion of the multiple-choice and free-response sections of, the exam are provided, along with totals for cach section and the composite score otal. With these tables and special statistical tables presenting grade distributions from previous years, the CEC can compare the exam at hand to results of other years For each composite score, a cable summarizes student performance on all sections of the exam. | Finally, on the basis of professional judgment regarding the quality of performance represented by the achieved scores, the CEC decermines the candidates’ final AP grades. See Table 4.3 for the 1997 AP Statistics Exam grade distributions. If you'te interested in more detailed information about this process, please see the “Technical Cornet” of our website: www.collegeboard.org/ap. There youl also find information about how che AP exams are developed, how validity and reliability studies are conducted, and other nuts-and-boles data on all AP subjectsTable 4.2 — Scoring Worksheet A x y)* 142865 0 Number correct Number wrong Multiple-Choice Weighted (out of 35) Score Section I m (Round to Score nearest whole 5 umber Iles than . zee, enter 2670.) fT Seite Mee Wal i srsaetss : Question 1 x 1.875 = S : Tout ora Do netroundh = Question 2 X 1.875 =_ ae . (outar ay {Do not rounah . uestion 3 x 1.875 = 7 a (oat oray 9 ean _ estion 4 x 1875 = : | a (out oray > eee A | . | uestion 5 x 1.875 = 2 } See 75 - en . | Question 6 x 1,562 eto Tout oF Sum = ‘Wonstrounay Weighted Section II (Oo not round.) (eeiniseicesrscia’ ‘Weighted Weighted ~~ Composite Score s Section IT (Round to the nearest ‘Score ‘whole number) Score AP Grade Composite Score Range* 68-100 54-67 41-53 29-40 0-28 =Nnona “The candidates’ scores are weighted according to formulas determined in advance ‘2ach year by the Development Committee to yield raw composite scores: the Chief Faculty Consultant is responsible for ‘converting composite scares to the 5-point AP scale.Table 4.3 — Grade Distributions More than 62% of che candidates earned an AP grade of 3 or higher. Extremely well qualified Well qualified 4 Qualified 3 Possibly qualified 2 No recommendation 1 Total Number of Students 7.646 Mean Grade 2.97 Standard Deviation 1,33 Table 4.4 — Section | Scores and AP Grades This table gives che probabilities that a student would receive a particular grade on the 1997 AP Statistics Exam given that studer ’s score on the multiple-choice section. fod Cre 30.10 35, 0.0% 0.0% 0.6% 19.6% PB 13.7% 25 t0.29. 0.0% 0.4% 19.4% 60.8% 193% 23.7% 211024 0.0% 122% oka 03% 20.1% 15 t0 20 10.2% 60.3% 28.1% 0.0% : 24.1% Ow 14 85.4% 14.0% 0.6% oo oe ee Toral 18.1% 196% 245% 221% 15.6% 100.0% 92 |Studies College Comparab Because the 1997 exam was the first one developed for statistics, a comparability study was done. In this study, college students enrolled in introductory statistics courses equivalent to the AP Statistics course were given amini-version of the exam. These mini-versions contained a subset of the questions in the exam, The scores obtained by the college students and the grades they received in their course were used to help deter- mine the appropriate AP grade for the AP students taking the examination, The AP Program has conducted college grade comparability studies in all other AP subjects as well As with Statistics, these studies compared the perfor- ‘mance of AP Exam candidates with that of college students in related courses who have taken the AP Exam. sa the end of their course. In general, AP cuspoints are selected so that the lowest AP 5 is equivalent to the average A student in college, the lowest AP 4 equivalent to the average B student, and the lowest AP 3 equivalent to the average C student (see figure below). ee eee 5 A 4 B 3 c 2 D 1 ‘To ensiue comparability of grades from year to year and to maintain a certain level of difficulty, some multiple-choice questions from previous AP Scatistics exams will be included on each new examination, Reminders for All Grade Report Recipients AP Examinations are designed to provide accurate assessments of achievement. However, any examination has limitations, especially when used for purposes other than those intended. Presented here are some suggestions for teachers to aid in the use and interpretation of AP grades. AP Examinations are developed and evaluated independently of each other. They are linked only by common purpose, format, and method of reporting results. Therefore, comparisons should not be made between grades on differenc AP Examinations. An AP grade in one subject may not have the same meaning as the same AP grade in another subject, just as national and college standards vary from one discipline to another. AP grades are not exactly comparable to college course geades. However, the AP Program conducts research studies every few years in cach AP subject to ensure that the AP grading standards are compa- rable to those used in colleges with similar courses | The confidentiality of candidace grade reports should be recognized and maintained. All individu- als who have access to AP grades should be aware of the confidential nacure of the grades and agree to maineain their security. In addition, school districts and states should not release data about high school performance without the school's permission. @ AP Examinations are not designed as instruments for teacher or school evaluation. A large number of factors influence AP Exam performance in a particular course or school in any given year. As a result, differences in AP Exam performance should be carefully studied before being actributed co the teacher or school. Where evaluation of AP students, ceachers, or courses is desired, local evaluation models should be developed. An important aspect of any evaluation model is the use of an appropriate method of comparison or frame of reference to account for yearly changes in student composition and ability, as well as local differences in resources, educational ‘methods, and socioeconomic factors. 93|The “Report to AP Teachers” can be a useful diagnostic tool in reviewing course results. This report identifies areas of strengch and weakness for each AP course. This information may also help to guide your students in identifying their own strengths and weaknesses in preparation for future study. (See below for information on how to obtain this report.) Many factors can influence course results. AP Exam performance may be due to the degree of agreement berween your course and the course defined in the relevant AP Course Description, use of different instructional methods, differences in emphasis or preparation on particular parts of the examination, differences in pre-AP curriculum, or differences in student background and preparation in comparison with the national group. Reporting AP Grades ‘The results of AP Examinations are disseminated in several ways to candidates, their secondary schools, and the colleges they select. College and candidate grade reports contain 2 cumulative record of all grades earned by the candidate on AP Exams during the current or previous years. These reports are sent in early July. (School grade reports are sent shortly thereafter.) Gcoup results for AP Examinations are available to AP teachers whenever five or more candidates at a school have taken a particular AP Exam. This “Report to AP Teachers” provides useful informa- tion comparing local candidate performance with that of the total group of candidates taking an exam, as well as details on different subsections of the exam. 94 Several other reports produced by the AP Program provide summary information on AP Examinations. State and National Reports show the distribution of grades obtained on each AP Exam for all candidates and for subsets of candidates broken down by sex and by ethnic group. The Program also produces a one-page suramary of AP grade distributions for all exams in a given year. For information on any of the above, please call AP Services at (609) 771-7300 or contact them via e-mail at apexams@ets.org. Purpose of AP Grades AP grades are intended to allow part ipacing colleges and universities to award college credit, advanced placement, or both to qualified students. In general, an AP grade of 3 or higher indicates sufficient mastery of course content to allow placement in the succeeding college course, or credit for and exemption from a college course comparable to the AP course. Credit and placement policies are determined by each college or university, however, and students should be urged to contact their colleges directly to ask for specific Advanced Placement policies in writing.IIL AP Publications and Videos a ‘A number of AP publications and videos are available to help students, parents, AP Coordinators, and high school and college faculty learn more about the AP Program and its courses and exams. To sort our those publications that may be of particular use o you, refer to the following key: Students and Parents SP ‘Teachers Ty AP Coordinators and Administrators A College Faculty ci You can order many items online through the AP Aisle of the College Board Online store at hetp:/ebweb2.collegeboard.org/shopping!. Alternatively, call AP Order Services at (609) 771-7243. ‘American Express, VISA, and MasterCard are accepted for payment. Ifyou are mailing your ordes, send it to the ‘Advanced Placement Program, Dept. E-05, BO. Box 6670, Princeton, NJ 08541-6670. Payment must accompany all orders nor on an insticutional purchase order or credie card, and checks should be made payable to the College Board. The College Board pays fourth-class book rate postage (or its equivalent) on all prepaid orders; you should allow between four and six weeks for delivery. Postage will be charged on all orders requiring billing and/or requesting a faster method of shipment. Publications may be returned within 30 days of receipt if postage is prepaid and publications are in resalable condition and still in print. Unless otherwise specified, orders will be filled with the currently available editions prices are subject to change without notice. AP Bulletin for Students and Parents: Free SP This bulletin provides a general description of the AP Program, including policies and procedures for preparing to take the exams, and registering for the ‘AP courses. It describes each AP Exam, lists the advan- tages of taking the exams, describes the grade and award options available to students, and includes the upcom- ing exam schedule. College and University Guide to the AP Program: $10 CA This guide is intended to help college and university faculty and administrators understand the benefits of having a coherent, equitable AP policy. Topics included are validity of AP grades; developing and maintaining scoring standards; ensuring equivalent achievement; state legislation supporting AP; and quantitative profiles of AP students by each AP subject. The College Handbook with College Explorer” CD-ROM: $25.95 SRTAC Includes brief outlines of AP placement and er policies at ewo- and four-year colleges across the country. Noves number of freshmen granted placement and/or credit for AP in the prior yea Course Descriptions: $12 SRTAC Course Descriptions provide an outline of the AP course content, explain the kinds of skills students are expected to demonstrate in the corresponding introduc~ tory college-level course, and describe the AP Exam. ‘They also provide sample mulciple-choice questions with an answer key, as well as sample free-response questions, A set of Course Descriptions is available for $100. Not included in this set are Course Descriptions for Computer Science, Government and Politics, and Statistics, which are available for downloading from the AP section of the College Board website (fice of charge) Five-Year Sct of Free-Response Questions: $5 T. This is our no-fiills publication. Each booklet contains copies of al the free-response questions from the last five exams in its subject; nothing more, nothing less. Collectively, the questions represent a comprehensive sampling of the concepts assessed on the exam in recent years and will give teachers plency of materials to use for essay-writing or problem-solving practice during the year (If there have been any content changes to the exam in the past five years, it will be noted on the cover of the booklet.) =Grading, Interpreting, and Using Advanced Placement Examinations: Free AGT A booklet containing information on the develop- ment of scoring scandards, the AP Reading, grade- setting procedures, and suggestions on how to interpret AP grades Guide to the Advanced Placement Program: Free A Written for both administrators and AP Coordinators, this guide provides general information about AP, such as how to organize an AP program at your high school, the kind of training and suppore that is available for AP teachers, and a look at che AP Exams and grades. ‘The second section contains more specific details about testing procedures and policies and is intended for AP Coordinators. ivided into two sections. The first section Released Exams: $20 T About every four yeats, on a staggered schedule, the AP Program releases a complete copy (multiple-choice and free-response sections) of each exam, as in the case of the 1997 Statistics Exam. Packets of 10 ($30): For each subject with a released exam, you can purchase a packet of 10 copies of that year's exams for use in your classroom (e.g,, to simulate an AP exam administration). Secondary School Guide to the AP Program: s10 This guide is a comprehensive consideration of the AP Program. It cavers topics such as: developing or expanding an AP programs gaining faculty, adminisera- tion, and community support; AP grade reports, their use and interpretation; AP Scholar Awardss receiving college credie for AP; AP teacher training resources; descriptions of successful AP programs in nine schools around che country; and “Voices of Experience,” a collection of ideas and tips from AP teachers and administrator. AT ‘Videoconference Tapes: $15 TC AP conducts live, interactive videoconferences for various subjects, enabling AP teachers and students to talk directly with the Development Committees that design the AP Exams. Tapes of these events are available in VHS format and are approximately 90 minutes long. ‘Teacher's Guides: $12 T ‘Whether you're about to teach an AP course for the first time, or you've done it for years but would like to get some fresh ideas for your classroom, the Teacher's Guide can be your mentor. It contains syllabi developed by high school reachers currencly ceaching the AP course and college faculty who teach the equivalent course at their institution. Along with detailed course outlines and innovative teaching tips, you'll also find extensive lists of recommended teaching resources. AP Pathway to Success (video, available in English and Spanish): $15 SRT, A,C This 25-minute-long video takes a look at the AP Program chrough the eyes of people who know AP: students, parents, teachers, and college admissions staff ‘They answer such questions as “Why Do Ie”, “Who Teaches AP Courses?”, and “Is AP For You?”. College students discuss the advantages they gained through taking AP, such as academic selfconfidence, writing skills, and course credit. AP teachers explain what the challenge of teaching AP courses means to them and their school, and admissions staf explain how they view students who have stretched themselves by taking AP Exams. There is also a discussion of the impact that an AP program has on an entire school and its community, and a look at resources available to help AP teachers, such as regional workshops, teacher conferences, and What's in a Grade? (video): $15 Be AP Exams are composed of multiple-choice questions (scored by computer), and free-response questions that are scored by qualified professors and teachers. This video presents a behind-the-scenes look at the scoring, process featuring footage shot on location at che 1992 ‘AP Reading at Clemson University and other Reading sites. Using the AP European History Exam as a basis, the video documents the scoring process. Ir shows AP faculty consultants in action as they engage in scholarly debate to define precise scoring standards, then train others to recognize and apply chose standards. Footage of other subjects, interviews with AP faculty consule- ants, and explanatory graphics round out the video. [96 |Umi eats e (es) 1996-97 Development Committee : Rosemary Roberts, Chair Daniel Teague . Bowdoin College North Carolina School of Brunswick, ME ‘Science and Mathematics Durham, NC Fred ©. Djang Choate Rosemary Hall Jessica M. Utts Wallingford, CT ‘University of California: Christopher R. Olsen Walter O. Walker George Washington Eckerd College High School St. Petersburg, FL Cedar Rapids, 1A Ann E. Watkins Dian C. Resnick California State University: Bellaire Senior High School Northridge Houston, TX Chief Faculty Consultant: Richard L, Scheaffer University of Florida Gainesville ETS Consultants: Jeff Haberstroh “Michael Ponisciak