AP Statistics Premium, 2023-2024: 9 Practice Tests + Comprehensive Review (2023-2024)

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APStatisticsPremium2023–2024Martin Sternstein, Ph.D.AP®is a registered trademark of the College Board, which was not involved in the production of, anddoes not endorse, this product.®

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ACKNOWLEDGMENTSThanks to Samantha Karasik, editor at Kaplan, for her guidance. Dawn Dentato and Paul Buckleyhave been of immense editorial help with proofreading this edition, and for that I am extremelygrateful. Thanks to my brother, Allan, my sister-in-law, Marilyn, my sons, Jonathan and Jeremy, mydaughters-in-law, Asia and Cheryl, and my grandchildren, Jaiden, Jordan, Josiah, Luna, Jayme, andLayla, for their heartfelt love and support. Most of all, thanks are due to my wife, Faith, whose love,warm encouragement, and always calm and optimistic perspective on life provide a homeenvironment in which deadlines can be met and goals easily achieved. My sincere appreciation goesto the participants who have attended my AP Statistics workshops for teaching me just as much as Ihave taught them, and special thanks for their many useful suggestions are due to the followingexceptional teachers:David BockPaul BuckleyDawn DentatoJared DerksenSarah JohnsonLee KuceraLaura MarshallBrendan MurphyLeigh NataroKenn PendletonAdam RiaziPenny SmeltzerDaren StarnesJosh TaborJane ViauDawn WhiteLuke WilcoxDash Young-SaverIthaca High School, Ithaca, NY (retired)Gonzaga College High School, Washington, DCSomers High School, Lincolndale, NY (retired)Rancho Cucamonga High School, Rancho Cucamonga, CAGrand Blanc High School, Grand Blanc, MIUniversity of California, Irvine, CAPhillips Exeter Academy, Exeter, NHJohn Bapst Memorial High School, Bangor, MEMoravian College, Bethlehem, PAMontgomery College, Germantown, MDCabell Midland High School, Ona, WVAustin Peace Academy, Austin, TXThe Lawrenceville School, Lawrenceville, NJCanyon del Oro High School, Oro Valley, ArizonaFrederick Douglass Academy, New York, NYSilver Lake Regional High School, Kingston, MAEast Kentwood High School, Kentwood, MIKIPP University Prep High School, San Antonio, TXMartin SternsteinIthaca College

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Spring 2022© Copyright 2022, 2020, 2019, 2017, 2015, 2013, 2012, 2010, 2007 by Kaplan North America d/b/aBarron’s Educational Series© Copyright 2004, 2000, 1998 by Kaplan North America d/b/a Barron’s Educational Series, under thetitleHow to Prepare for the AP Advanced Placement Exam in Statistics.All rights reserved under International and Pan-American Copyright Conventions. By payment of therequired fees, you have been granted the non-exclusive, non-transferable right to access and readthe text of this eBook on screen. No part of this text may be reproduced, transmitted, downloaded,decompiled, reverse engineered, or stored in or introduced into any information storage andretrieval system, in any form or by any means, whether electronic or mechanical, now known orhereinafter invented, without the express written permission of the publisher.Published by Kaplan North Americad/b/a Barron’s Educational Series1515 W Cypress Creek RoadFort Lauderdale, FL 33309www.barronseduc.comISBN: 978-1-5062-8010-310 9 8 7 6 5 4 3 2 1ABOUT THE AUTHORDr. Martin Sternstein, Professor Emeritus at Ithaca College, was honored by Princeton Review asone of the nation’s “300 Best College Professors.” He is a long-time College Board consultant andhas been a Reader and Table Leader for the AP Statistics exam for many years. He has stronginterests in national educational and social issues concerning equal access to math education forall. For two years, he was a Fulbright Professor in Liberia, West Africa, after which he developed apopular “Math in Africa” course, and he is the only mathematician to have given a presentation atthe annual Conference on African Linguistics. He also taught the first U.S. course for college credit inchess theory.

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Table of ContentsHow to Use This BookBarron’s Essential 5Exam OverviewPART 1: DIAGNOSTIC TESTDiagnostic TestAnswer KeyAnswer ExplanationsAP Score for the Diagnostic TestStudy Guide for the Diagnostic Test Multiple-ChoiceQuestionsPART 2: UNITS REVIEWUNIT 1. Exploring One-Variable DataCategorical VariablesRepresenting a Quantitative Variable with Tables and GraphsDescribing the Distribution of a Quantitative VariableQuiz 1Summary Statistics for a Quantitative VariableGraphical Representations of Summary StatisticsComparing Distributions of a Quantitative VariableQuiz 2The Normal DistributionQuiz 3SummaryUNIT 2. Exploring Two-Variable DataTwo Categorical VariablesQuiz 4Two Quantitative VariablesCorrelationLeast Squares RegressionResidualsOutliers, Influential Points, and LeverageMore on RegressionTransformations to Achieve Linearity

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Quiz 5Quiz 6SummaryUNIT 3: Collecting DataRetrospective Versus Prospective Observational StudiesBiasSampling MethodsSampling VariabilityQuiz 7Experiments Versus Observational StudiesThe Language of ExperimentsReplication and Generalizability of ResultsInference and ExperimentsQuiz 8SummaryUNIT 4. Probability, Random Variables, and ProbabilityDistributionsThe Law of Large NumbersBasic Probability RulesMultistage Probability CalculationsQuiz 9Random Variables, Means (Expected Values), and StandardDeviationsMeans and Variances for Sums and Differences of SetsMeans and Variances for Sums and Differences of RandomVariablesTransforming Random VariablesQuiz 10Binomial DistributionGeometric DistributionQuiz 11Cumulative Probability DistributionSummaryUNIT 5. Sampling DistributionsNormal Distribution CalculationsQuiz 12Central Limit Theorem

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Biased and Unbiased EstimatorsSampling Distribution for Sample ProportionsSampling Distribution for Differences in Sample ProportionsSampling Distribution for Sample MeansSampling Distribution for Differences in Sample MeansSimulation of a Sampling DistributionQuiz 13SummaryUNIT 6. Inference for Categorical Data: ProportionsThe Meaning of a Confidence IntervalConditions for InferenceConfidence Interval for a ProportionQuiz 14Quiz 15Logic of Significance TestingSignificance Test for a ProportionConfidence Interval for the Difference of Two ProportionsSignificance Test for the Difference of Two ProportionsQuiz 16Quiz 17SummaryUNIT 7. Inference for Quantitative Data: MeansThet-distributionConfidence Interval for a MeanQuiz 18Significance Test for a MeanConfidence Interval for the Difference of Two MeansSignificance Test for the Difference of Two MeansPaired DataQuiz 19Simulations andP-ValuesQuiz 20More on Power, Type I Errors, and Type II ErrorsQuiz 21Confidence Intervals Versus Hypothesis TestsSummaryUNIT 8. Inference for Categorical Data: Chi-Square

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Chi-Square Test for Goodness-of-FitChi-Square Test for IndependenceChi-Square Test for HomogeneityQuiz 22SummaryUNIT 9. Inference for Quantitative Data: SlopesSampling Distribution for the SlopeConfidence Interval for the Slope of a Least SquaresRegression LineHypothesis Test for Slope of Least Squares Regression LineQuiz 23Quiz 24SummaryPART 3: FINAL REVIEWFinal ReviewSelecting an Appropriate Inference ProcedureQuiz 25Quiz 26Statistical Insights into Social IssuesQuiz 27Quiz 28The Investigative Task: Free-Response Question 6Quiz 2950 Misconceptions50 Common Errors on the AP Exam50 AP Exam Hints, Advice, and RemindersPART 4: PRACTICE TESTSPractice Test 1Answer KeyAnswers and ExplanationsPractice Test 2Answer KeyAnswers and ExplanationsPractice Test 3Answer KeyAnswers and ExplanationsPractice Test 4

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Answer KeyAnswers and ExplanationsPractice Test 5Answer KeyAnswers and ExplanationsPART 5: APPENDICESAppendicesFormulasGraphical DisplaysChecking Assumptions for InferenceIndependenceMore on ResidualsAnswer Explanations for Quizzes 1–29AP Scoring GuideBasic Uses of the TI-84Basic Uses of the Casio PrizmBasic Uses of the HP PrimeTable A: Standard Normal ProbabilitiesTable B:t-Distribution Critical ValuesTable C: χ2Critical Values

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How to Use This BookThis book provides comprehensive review and extensive practice for thelatest AP Statistics course and exam.ABOUT THE EXAMStart with the Exam Overview, which outlines the exam format. Familiarizeyourself with all of the units covered on this test, review the differentquestion types, and learn how the exam will be scored.DIAGNOSTIC TESTNext, take the full-length diagnostic test in Part 1 to determine whichtopics you know well and which ones you may want to brush up on.Complete the entire test, and then check all of the answer explanations,especially for any questions you may have missed. Then, consult the StudyGuide for units in the book that you should focus your review on.REVIEW AND PRACTICEStudy all 9 chapters in Part 2, which are organized according to the nineunits of AP Statistics, and cover the topics recommended by the APStatistics Development Committee. Every chapter includes Learning

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Objectives that will be covered, a review of each topic, dozens of figuresand tables that illustrate key concepts, and end-of-chapter summaries.Interspersed among these units are 29 quizzes (mini-AP exams with bothmultiple-choice and free-response questions), which should be used asprogress checks.Then, consult Part 3, the Final Review, which has several invaluablesections.PRACTICE TESTS“Selecting an Appropriate Inference Procedure” offers hints on inferencerecognition followed by two quizzes on naming the procedure to use,defining parameters, listing conditions to be checked, and statinghypotheses, if appropriate.“Statistical Insights into Social Issues” includes two quizzes ofcomprehensive review questions that cover the whole AP Statisticscurriculum. These quizzes aim to give an appreciation of the power ofstatistics and show how this subject gives insights into some of society’smost pressing issues.“The Investigative Task” helps you prepare for free-response Question 6,which counts for one-eighth of your total grade on the exam; there arethree illustrative examples followed by a quiz with seven practiceinvestigative tasks.“50 Misconceptions,” “50 Common Errors on the AP Exam,” and “50 APExam Hints, Advice, and Reminders” provide tips to remember and pitfallsto avoid on test day.

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There are five full-length practice tests in the book that mirror the actualexam in format, content, and level of difficulty. Each test is followed bydetailed answers and explanations for all questions.APPENDICESThe end of this book consists of a series of helpful appendices, includingthe answers and explanations for all quizzes, important formulas to know,basic uses for common graphing calculators, and much more. Be sure toreview these sections before completing your review.ONLINE PRACTICEThere are also three additional full-length practice tests online where allquestions are answered and explained. You may take these tests inpractice (untimed) mode or in timed mode.FOR STUDENTSThis book is intended both as a topical review during the year and as a finalreview in the weeks before the AP exam. Study the text and illustrativeexamples carefully, and try to complete the practice quiz problems beforereferring to the solutions. Simply reading the detailed explanationswithout first striving to work through the questions on your own is not thebest approach. Remember,mathematics is not a spectator sport!Usethe practice quizzes at appropriate times throughout the school year, andyou will develop confidence and a deeper understanding of the material.

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A good piece of advice is to develop critical practices (like checkingassumptions and conditions), acquire strong technical skills, and alwayswrite clear and thorough, yet to the point, interpretations and conclusionsin context. Final answers to most problems should not be numbers, butrather sentences explaining and analyzing numerical results. To helpdevelop skills and insights to tackle AP free-response questions (whichoften choose contexts students haven’t seen before), read newspapers andmagazines, and figure out how to apply what you are learning to betterunderstand articles that reference numbers, graphs, and studies.The AP Statistics course is one of the fastest growing and mostimportant courses offered in the high school curriculum. If you work withyour teacher and study hard, you will find this to be an enjoyable course,you will do well on the AP exam, and you will develop into a morethoughtful citizen of this world! One day, when you’re a data scientist, anengineer, a doctor or nurse, a manager, or whatever it is you do, you maylook back on the AP exam as only a distant memory, but you’ll rememberthe truly important things you learned in your AP Statistics class. You’llremember how to think critically and compassionately about the worldaround you and how to communicate your knowledge, insights, anddiscoveries; these are skills you’ll carry with you for the rest of your life.FOR TEACHERSThis book is fully aligned with the nine units and exam format outlined inthe latest AP Statistics Course and Exam Description. Ideally, eachindividual unit review, paired with practice quiz problems, should beassigned after the unit has been covered in class. The full-length practicetests should be reserved for final review shortly before the AP exam.

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Barron’s Essential 5As you review the content in this book and work toward earning that5onyour AP STATISTICS exam, here are five things that youMUSTknow:Graders want to give you credit—help them!Make them understandwhatyou are doing,whyyou are doing it, andhowyou are doing it.Don’t make the reader guess at what you are doing.1.Communicationis just as important as statistical knowledge!Be sure you understandexactly what you are being asked to do orfind or explainandapproach each problem systematically.Some problems look scary on first reading but are not overly difficultand are surprisingly straightforward. Questions that take you beyondthe scope of the AP curriculum will be phrased in ways that you shouldbe able to answer them based on what you have learned in your APStatistics class.Nakedorbald answerswill receive little ornocredit. You must showwhere answers come from.On the other hand, don’t give more than one solution to the sameproblem—you will receive credit only for the weaker one.Random sampling and random assignment are different ideas.2.Random sampling is the use of chance in selecting a sample from apopulation and is critical in being able to generalize from a sample to apopulation.Asimple random sample(SRS) is when every possible sample of a—

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