Elementary Statistics: A Step-by-Step Approach (2009) PDF

blu34978_fm.qxd 9/11/08 10:12 AM Page i S E V E N T H E D I T I O N Elementary Statistics A Step by Step Approach...

blu34978_fm.qxd 9/11/08 10:12 AM Page i S E V E N T H E D I T I O N Elementary Statistics A Step by Step Approach Allan G. Bluman Professor Emeritus Community College of Allegheny County blu34978_fm.qxd 9/11/08 10:12 AM Page ii ELEMENTARY STATISTICS: A STEP BY STEP APPROACH, SEVENTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. Previous editions © 2007, 2004, 2001, 1998, and 1995. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 VNH/VNH 0 9 8 ISBN 978–0–07–353497–8 MHID 0–07–353497–8 ISBN 978–0–07–333121–8 (Annotated Instructor’s Edition) MHID 0–07–333121–X Editorial Director: Stewart K. Mattson Sponsoring Editor: Dawn R. Bercier Director of Development: Kristine Tibbetts Developmental Editor: Michelle Driscoll Marketing Manager: John Osgood Project Manager: April R. Southwood Lead Production Supervisor: Sandy Ludovissy Senior Media Project Manager: Sandra M. Schnee Designer: Tara McDermott Cover Designer: Rick D. Noel (USE) Cover Image: © Atlantide Phototravel/Corbis Senior Photo Research Coordinator: Lori Hancock Supplement Producer: Mary Jane Lampe Compositor: ICC Macmillan Inc. Typeface: 10.5/12 Times Roman Printer: Von Hoffmann Press The credits section for this book begins on page 815 and is considered an extension of the copyright page. Library of Congress Cataloging-in-Publication Data Bluman, Allan G. Elementary statistics : a step by step approach / Allan G. Bluman. — 7th ed. p. cm. Includes bibliographical references and index. ISBN 978–0–07–353497–8 — ISBN 0–07–353497–8 (hard copy : acid-free paper) 1. Statistics—Textbooks. I. Title. QA276.12.B59 2009 519.5—dc22 2008030803 www.mhhe.com blu34978_fm.qxd 9/11/08 10:12 AM Page iii Brief Contents CHAPTE R 1 The Nature CHAPTE R 8 Hypothesis of Probability Testing 399 and Statistics 1 CHAPTE R 9 Testing the Difference CHAPTE R 2 Frequency Between Two Means, Distributions Two Proportions, and and Graphs 35 Two Variances 471 CHAPTE R 3 Data Description 103 CHAPTE R 10 Correlation and Regression 533 CHAPTE R 4 Probability and Counting Rules 181 CHAPTE R 11 Other Chi-Square Tests 589 CHAPTE R 5 Discrete Probability Distributions 251 CHAPTE R 12 Analysis of Variance 627 CHAPTE R 6 The Normal Distribution 299 CHAPTE R 13 Nonparametric Statistics 669 CHAPTE R 7 Confidence Intervals and Sample CHAPTE R 14 Sampling and Size 355 Simulation 717 All examples and exercises in this textbook (unless cited) are hypothetical and are presented to enable students to achieve a basic understanding of the statisti- cal concepts explained. These examples and exercises should not be used in lieu of medical, psychological, or other professional advice. Neither the author nor the publisher shall be held responsible for any misuse of the information presented in this textbook. iii blu34978_fm.qxd 9/11/08 10:12 AM Page iv iv Brief Contents APPE N DIX A Algebra Review 751 APPE N DIX D Data Bank 797 APPE N DIX B–1Writing the Research APPE N DIX E Glossary 805 Report 757 APPE N DIX F Bibliography 813 APPE N DIX B–2 Bayes’ Theorem 759 APPE N DIX G Photo Credits 815 APPE N DIX B–3 Alternate Approach to the Standard Normal Distribution 763 APPE N DIX H Selected Answers SA–1 APPE N DIX C Tables 767 Index I–1 blu34978_fm.qxd 9/11/08 10:12 AM Page v Contents Preface ix 2–2 Histograms, Frequency Polygons, and Ogives 51 The Histogram 51 CHAPTE R 1 The Frequency Polygon 53 The Nature of Probability The Ogive 54 and Statistics 1 Relative Frequency Graphs 56 Introduction 2 Distribution Shapes 59 2–3 Other Types of Graphs 68 1–1 Descriptive and Inferential Statistics 3 Bar Graphs 69 1–2 Variables and Types of Data 6 Pareto Charts 70 1–3 Data Collection and Sampling Techniques 9 The Time Series Graph 71 Random Sampling 10 The Pie Graph 73 Misleading Graphs 76 Systematic Sampling 11 Stem and Leaf Plots 80 Stratified Sampling 12 Summary 94 Cluster Sampling 12 Other Sampling Methods 13 1–4 Observational and Experimental Studies 13 CHAPTE R 3 1–5 Uses and Misuses of Statistics 16 Data Description 103 Suspect Samples 17 Introduction 104 Ambiguous Averages 17 3–1 Measures of Central Changing the Subject 17 Tendency 105 Detached Statistics 18 The Mean 106 Implied Connections 18 The Median 109 Misleading Graphs 18 The Mode 111 Faulty Survey Questions 18 The Midrange 114 1–6 Computers and Calculators 19 The Weighted Mean 115 Summary 25 Distribution Shapes 117 3–2 Measures of Variation 123 Range 124 CHAPTE R 2 Population Variance and Standard Deviation 125 Sample Variance and Standard Deviation 128 Frequency Distributions Variance and Standard Deviation and Graphs 35 for Grouped Data 129 Introduction 36 Coefficient of Variation 132 2–1 Organizing Data 37 Range Rule of Thumb 133 Categorical Frequency Distributions 38 Chebyshev’s Theorem 134 Grouped Frequency Distributions 39 The Empirical (Normal) Rule 136 v blu34978_fm.qxd 9/11/08 10:12 AM Page vi vi Contents 3–3 Measures of Position 142 5–3 The Binomial Distribution 270 Standard Scores 142 5–4 Other Types of Distributions (Optional) 283 Percentiles 143 The Multinomial Distribution 283 Quartiles and Deciles 149 The Poisson Distribution 284 Outliers 151 The Hypergeometric Distribution 286 3–4 Exploratory Data Analysis 162 Summary 292 The Five-Number Summary and Boxplots 162 6 Summary 171 CHAPTE R The Normal Distribution 299 CHAPTE R 4 Introduction 300 Probability and Counting 6–1 Normal Distributions 302 Rules 181 The Standard Normal Introduction 182 Distribution 304 4–1 Sample Spaces and Finding Areas Under the Standard Normal Probability 183 Distribution Curve 305 Basic Concepts 183 A Normal Distribution Curve as a Probability Classical Probability 186 Distribution Curve 307 Complementary Events 189 6–2 Applications of the Normal Empirical Probability 191 Distribution 316 Law of Large Numbers 193 Finding Data Values Given Specific Probabilities 319 Subjective Probability 194 Determining Normality 322 Probability and Risk Taking 194 6–3 The Central Limit Theorem 331 4–2 The Addition Rules for Probability 199 Distribution of Sample Means 331 4–3 The Multiplication Rules and Conditional Probability 211 Finite Population Correction Factor (Optional) 337 The Multiplication Rules 211 Conditional Probability 216 6–4 The Normal Approximation to the Binomial Distribution 340 Probabilities for “At Least” 218 Summary 347 4–4 Counting Rules 224 The Fundamental Counting Rule 224 Factorial Notation 227 CHAPTE R 7 Permutations 227 Confidence Intervals Combinations 229 and Sample Size 355 4–5 Probability and Counting Rules 237 Introduction 356 Summary 242 7–1 Confidence Intervals for the Mean When s Is Known CHAPTE R 5 and Sample Size 357 Confidence Intervals 358 Discrete Probability Sample Size 363 Distributions 251 7–2 Confidence Intervals for the Mean Introduction 252 When s Is Unknown 370 5–1 Probability 7–3 Confidence Intervals and Sample Size Distributions 253 for Proportions 377 5–2 Mean, Variance, Standard Deviation, Confidence Intervals 378 and Expectation 259 Sample Size for Proportions 379 Mean 259 7–4 Confidence Intervals for Variances Variance and Standard Deviation 262 and Standard Deviations 385 Expectation 264 Summary 392 blu34978_fm.qxd 9/11/08 10:12 AM Page vii Contents vii CHAPTE R 8 Determination of the Regression Line Equation 552 Hypothesis Testing 399 10–3 Coefficient of Determination and Standard Introduction 400 Error of the Estimate 565 8–1 Steps in Hypothesis Types of Variation for the Regression Model 565 Testing—Traditional Coefficient of Determination 568 Method 401 Standard Error of the Estimate 568 8–2 z Test for a Mean 413 Prediction Interval 570 P-Value Method for Hypothesis Testing 418 10–4 Multiple Regression (Optional) 573 8–3 t Test for a Mean 427 The Multiple Regression Equation 575 8–4 z Test for a Proportion 437 Testing the Significance of R 577 8–5 x2 Test for a Variance or Standard Adjusted R 2 578 Deviation 445 Summary 582 8–6 Additional Topics Regarding Hypothesis Testing 457 Confidence Intervals and Hypothesis Testing 457 CHAPTE R 11 Type II Error and the Power of a Test 459 Other Chi-Square Tests 589 Summary 462 Introduction 590 11–1 Test for Goodness CHAPTE R 9 of Fit 591 Testing the Difference Test of Normality Between Two Means, Two (Optional) 596 Proportions, and 11–2 Tests Using Contingency Tables 604 Two Variances 471 Test for Independence 604 Introduction 472 Test for Homogeneity of Proportions 609 9–1 Testing the Difference Between Summary 619 Two Means: Using the z Test 473 9–2 Testing the Difference Between Two Means of Independent Samples: CHAPTE R 12 Using the t Test 484 Analysis of Variance 627 9–3 Testing the Difference Between Two Means: Introduction 628 Dependent Samples 491 12–1 One-Way Analysis of 9–4 Testing the Difference Between Variance 629 Proportions 503 12–2 The Scheffé Test 9–5 Testing the Difference Between and the Tukey Test 640 Two Variances 512 Scheffé Test 640 Summary 523 Tukey Test 642 Hypothesis-Testing Summary 1 531 12–3 Two-Way Analysis of Variance 645 Summary 659 CHAPTE R 10 Hypothesis-Testing Summary 2 667 Correlation and Regression 533 CHAPTE R 13 Introduction 534 Nonparametric 10–1 Scatter Plots and Statistics 669 Correlation 535 Introduction 670 Correlation 539 13–1 Advantages and 10–2 Regression 551 Disadvantages of Line of Best Fit 551 Nonparametric Methods 671 blu34978_fm.qxd 9/11/08 10:12 AM Page viii viii Contents Advantages 671 APPENDIX A Algebra Review 751 Disadvantages 671 Ranking 671 13–2 The Sign Test 673 APPENDIX B–1 Writing the Research Report 757 Single-Sample Sign Test 673 Paired-Sample Sign Test 675 13–3 The Wilcoxon Rank Sum Test 681 APPENDIX B–2 Bayes’ Theorem 759 13–4 The Wilcoxon Signed-Rank Test 686 13–5 The Kruskal-Wallis Test 691 13–6 The Spearman Rank Correlation Coefficient APPENDIX B–3 Alternate Approach to and the Runs Test 697 the Standard Normal Distribution 763 Rank Correlation Coefficient 697 The Runs Test 700 Summary 708 APPENDIX C Tables 767 Hypothesis-Testing Summary 3 714 CHAPTE R 14 APPENDIX D Data Bank 797 Sampling and Simulation 717 APPENDIX E Glossary 805 Introduction 718 14–1 Common Sampling Techniques 719 APPENDIX F Bibliography 813 Random Sampling 719 Systematic Sampling 723 APPENDIX G Photo Credits 815 Stratified Sampling 724 Cluster Sampling 726 Other Types of Sampling Techniques 727 APPENDIX H Selected Answers SA–1 14–2 Surveys and Questionnaire Design 734 14–3 Simulation Techniques and the Monte Carlo Method 737 Index I–1 The Monte Carlo Method 737 Summary 743 blu34978_fm.qxd 9/11/08 10:12 AM Page ix Preface Approach Elementary Statistics: A Step by Step Approach was written as an aid in the beginning statistics course to students whose mathematical background is limited to basic algebra. The book follows a nontheoretical approach without formal proofs, explaining concepts intuitively and supporting them with abundant examples. The applications span a broad range of topics certain to appeal to the interests of students of diverse backgrounds and include problems in business, sports, health, architecture, education, entertainment, political science, psychology, history, criminal justice, the environment, transportation, physical sciences, demographics, eating habits, and travel and leisure. About This While a number of important changes have been made in the seventh edition, the learn- Book ing system remains untouched and provides students with a useful framework in which to learn and apply concepts. Some of the retained features include the following: Over 1800 exercises are located at the end of major sections within each chapter. Hypothesis-Testing Summaries are found at the end of Chapter 9 (z, t, x2, and F tests for testing means, proportions, and variances), Chapter 12 (correlation, chi-square, and ANOVA), and Chapter 13 (nonparametric tests) to show students the different types of hypotheses and the types of tests to use. A Data Bank listing various attributes (educational level, cholesterol level, gender, etc.) for 100 people and several additional data sets using real data are included and referenced in various exercises and projects throughout the book. An updated reference card containing the formulas and the z, t, x2, and PPMC tables is included with this textbook. End-of-chapter Summaries, Important Terms, and Important Formulas give students a concise summary of the chapter topics and provide a good source for quiz or test preparation. Review Exercises are found at the end of each chapter. Special sections called Data Analysis require students to work with a data set to perform various statistical tests or procedures and then summarize the results. The data are included in the Data Bank in Appendix D and can be downloaded from the book’s website at www.mhhe.com/bluman. Chapter Quizzes, found at the end of each chapter, include multiple-choice, true/false, and completion questions along with exercises to test students’ knowledge and comprehension of chapter content. The Appendixes provide students with an essential algebra review, an outline for report writing, Bayes’ theorem, extensive reference tables, a glossary, and answers to all quiz questions, all odd-numbered exercises, selected even-numbered exercises, and an alternate method for using the standard normal distribution. ix blu34978_fm.qxd 9/11/08 3:11 PM Page x x Preface The Applying the Concepts feature is included in all sections and gives students an opportunity to think about the new concepts and apply them to hypothetical examples and scenarios similar to those found in newspapers, magazines, and radio and television news programs. Changes in This edition of Elementary Statistics is updated and improved for students and instruc- the Seventh tors in the following ways: Edition Over 300 new exercises have been added, most using real data, and many exercises incorporate thought-provoking questions requiring students to interpret their results. Titles have been given to each application example and each exercise problem to emphasize their real-world relevance. Six new Speaking of Statistics topics have been included. An explanation of bar graphs has been added to Chapter 2 since bar graphs are one of the most commonly used graphs in statistics, and they are slightly different from Pareto charts. Over 40 examples have been replaced with new ones, the majority using real data. Two graphs have been added to the explanation of the chi-square distribution in Chapter 7 to help clarify the nature of the distribution and how the distribution is related to the chi-square table. The Excel Technology Step by Step boxes have been updated to reflect Microsoft Excel 2007. The shortcut formula for the standard deviation has been changed. The formula used ! n#"X2 $ " #"X$ 2 now is s ! , which is the one used in most other statistics books. n#n " 1$ ! "X2 " [#"X$ 2%n] It also avoids the complex fraction used in the other formula s !. n"1 Many reviewers have stated that they like the first formula better than the second one. The cumulative standard normal distribution is used throughout the book. The null hypothesis is stated using the equals sign in all cases where appropriate. When s or s1 and s2 are known, the z tests are used in hypothesis testing. When s or s1 and s2 are unknown, the t tests are used in hypothesis testing. The F test for two variances is no longer used before the t test for the difference between two means when s1 and s2 are unknown. The Data Projects at the end of each chapter are all new and are specific to the areas of Business and Finance, Sports and Leisure, Technology, Health and Wellness, Politics and Economics, and Your Class. blu34978_fm.qxd 9/11/08 10:12 AM Page xi Preface xi Acknowledgments It is important to acknowledge the many people whose contributions have gone into the Seventh Edition of Elementary Statistics. Very special thanks are due to Jackie Miller of The Ohio State University for her provision of the Index of Applications, her exhaustive accuracy check of the page proofs, and her general availability and advice concerning all matters statistical. The Technology Step by Step sections were provided by Gerry Moultine of Northwood University (MINITAB), John Thomas of College of Lake County (Excel), and Michael Keller of St. Johns River Community College (TI-83 Plus and TI-84 Plus). I would also like to thank Diane P. Cope for providing the new exercises, Kelly Jackson for writing the new Data Projects, and Sally Robinson for error checking, adding technology-accurate answers to the answer appendix, and writing the Solutions Manuals. Finally, at McGraw-Hill Higher Education, thanks to Dawn Bercier, Sponsoring Editor; Michelle Driscoll, Developmental Editor; John Osgood, Marketing Manager; April Southwood, Project Manager; Amber Bettcher, Digital Product Manager; and Sandra Schnee, Senior Media Project Manager. Allan G. Bluman Special thanks for their advice and recommendations for revisions found in the Seventh Edition go to Stan Adamski, Owens Community College Thomas Fitzkee, Francis Marion University Olcay Akman, Illinois State University Kevin Fox, Shasta College Patty G. Amick, Greenville Technical College Dr. Tom Fox, Cleveland State Community College Raid Amin, University of West Florida Leszek Gawarecki, Kettering University Diana J. Asmus, Greenville Technical College Dana Goodwin, University of Central Arkansas John J. Avioli, Christopher Newport University C. Richard Gumina, Jr., Colorado State University Barb Barnet, University of Wisconsin, Platteville Shawn Haghighi, Lindenwood University Sr. Prof. Abraham Biggs, Broward Community Elizabeth Hamman, Cypress College College Dr. Willard J. Hannon, Las Positas College Wes Black, Illinois Valley Community College Robert L. Heiny, University of Northern Colorado William L. Blubaugh, University of Northern Todd Hendricks, Georgia Perimeter College Colorado Jada P. Hill, Richland College Donna Brouillette, Georgia Perimeter College Dr. James Hodge, Mountain State University Robert E. Buck, Slippery Rock University Clarence Johnson, Cuyahoga Community College David Busekist, Southeastern Louisiana University Craig Johnson, Brigham Young University—Idaho Ferry Butar Butar, Sam Houston State University Anne M. Jowsey, Niagara County Community Keri Catalfomo, TriCounty Community College College Lee R. Clendenning, Berry College Linda Kelly-Penny, Midland College Sarah Trattler Clifton, Southeastern Louisiana University Jong Sung Kim, Portland State University Jeff Edmunds, University of Mary Washington Janna Liberant, Rockland Community College SUNY Billy Edwards, University of Tennessee at Jackie MacLaughlin, Central Piedmont Community Chattanooga College C. Wayne Ehler, Ann Arundel Community College Rich Marchand, Slippery Rock University Hassan Elsalloukh, University of Arkansas at Little Steve Marsden, Glendale College Rock Michael McKenna, Louisiana State University blu34978_fm.qxd 9/11/08 10:12 AM Page xii xii Preface Ayrin C. Molefe, University of Central Arkansas Martha Tapia, Berry College Christina Morian, Lincoln University Sherry Taylor, Piedmont Technical College Alfred K. Mulzet, Florida Community College at William Trunkhill, Waubonsee Community College Jacksonville Jo Tucker, Tarrant County College–SE Humberto Munoz, Southern University and A&M Thomas Tunnell, Illinois Valley Community College College at Baton Rouge Christina Vertullo, Marist College Miroslaw Mystkowski, Gardner-Webb University Dr. Mahbobeh Vezvaei, Kent State University Michael A. Nasab, Long Beach City College Tilaka N. Vijithakumara, Illinois State University Jeanne Osborne, Middlesex County College Barbara B. Ward, Belmont University Elaine S. Paris, Mercy College William D. Warde, Oklahoma State University Suzie Pickle, St. Petersburg College Brenda Weak, Las Positas College Robert H. Prince, Berry College Glenn Weber, Christopher Newport University Aaron Robertson, Colgate University Daniel C. Weiner, Boston University Kim Gilbert, University of Georgia Jane-Marie Wright, Suffolk County Community Jason Samuels, BMCC College Salvatore Sciandra, Niagara County Community Yibao Xu, Borough of Manhattan Community College College, CUNY Lynn Smith, Gloucester County College Yi Ye, University of North Florida Dr. M. Jill Stewart, Radford University Jill S. Yoder, North Central Texas College Kagba Suaray, California State University, Quinhong Zhang, Northern Michigan University Long Beach James Zimmer, Chattanooga State Gretchen I. Syhre, Hawkeye Community College Special thanks for their advice and recommendations for revisions found in the Fifth and Sixth Editions go to Rosalie Abraham, Florida Community College-North Melody E. Eldred, State University College–Oneonta Anne Albert, University of Findlay Abdul Elfessi, University of Wisconsin–LaCrosse Trania Aquino, Del Mar College Gholamhosse Gharehgozlo Hamedani, Marquette Rona Axelrod, Edison Community College University Mark D. Baker, M.S., Illinois State University Joseph Glaz, University of Connecticut Sivanandan Balakumar, Lincoln University Liliana Gonzalez, University of Rhode Island– Kingston Naveen K. Bansal, Marquette University Rebekah A. Griffith, McNeese State University Freda Bennett, Massachusetts College of Liberal Arts Renu A. Gupta, Louisiana State University–Alexandria Matthew Bognar, University of Iowa Harold S. Hayford, Pennsylvania State University– Andrea Boito, Pennsylvania State University–Altoona Altoona Dean Burbank, Gulf Coast Community College Shahryar Heydari, Piedmont College Christine Bush, Palm Beach Community College–Palm Helene Humphrey, San Joaquin Delta College Beach Gardens Patricia Humphrey, Georgia Southern University Carlos Canas, Florida Memorial College Charles W. Johnson, Collin County Community James Condor, Manatee Community College–Plano College–Bradenton Jeffery C. Jones, County College of Morris Diane Cope, Washington & Jefferson College Anand Katiyar, McNeese State University Gregory Daubenmire, Las Positas College Brother Donald Kelly, Marist College blu34978_fm.qxd 9/11/08 10:12 AM Page xiii Preface xiii Dr. Susan Kelly, University of Wisconsin–La Crosse Don R. Robinson, Illinois State University Michael Kent, Borough of Manhattan Community Kathy Rogotzke, North Iowa Area Community College College–Mason City B. M. Golam Kibria, Florida International Deb Rumsey, The Ohio State University University–Miami Carolyn Shealy, Piedmont Technical College Hyun-Joo Kim, Truman State University Dr. J. N. Singh, Barry University Joseph Kunicki, University of Findlay George Smeltzer, Pennsylvania State University– Marie Langston, Palm Beach Community College– Abington Lakeworth Jeganathan Sriskandarajah, Madison Area Technical Susan S. Lenker, Central Michigan University College Benny Lo, DeVry University Diana Staats, Dutchess Community College Chip Mason, Belhaven College Richard Stevens, University of Alaska–Fairbanks Judith McCrory, Findlay University Richard Stockbridge, University of Wisconsin– Lynnette Meslinsky, Erie Community College Milwaukee Charles J. Miller, Jr., Camden County College Linda Sturges, SUNY Maritime College Carla A. Monticelli, Camden County College Klement Teixeira, Borough of Manhattan Community College Lindsay Packer, College of Charleston Diane Van Deusen, Napa Valley College Irene Palacios, Grossmont College Cassandra L. Vincent, Plattsburgh State Samuel Park, Long Island University–Brooklyn University Chester Piascik, Bryant University David Wallach, Findlay University Leela Rakesh, Central Michigan University Cheng Wang, Nova Southeastern University Fernando Rincón, Piedmont Technical College This page intentionally left blank blu34978_fm.qxd 9/11/08 10:13 AM Page xv Guided Tour: Features and Supplements 6 Each chapter begins with an outline and a list of learning objectives. The C H A P T E R objectives are repeated at the beginning of each section to help students focus on the concepts presented within that section. The Normal Distribution Tests quare Chi-S Objectives Outline Other er 11 Chapt 590 After completing this chapter, you should be able to Introduction 1 Identify distributions as symmetric or skewed. 6–1 Normal Distributions 2 Identify the properties of a normal distribution. 3 Find the area under the standard normal 6–2 Applications of the Normal Distribution distribution, given various z values. 6–3 The Central Limit Theorem 4 Find probabilities for a normally distributed variable by transforming it into a standard 6–4 The Normal Approximation to the Binomial normal variable. Distribution 5 Find specific data values for given percentages, using the standard normal Summary distribution. 6 Use the central limit theorem to solve problems involving sample means for large samples. 7 Use the normal approximation to compute probabilities for a binomial variable. les are princip f peas nd his o g e n e tics, a w a variety at had udied to gro eas th y 884), st spare time breeding p t the results Hereditor Mendel (18e2ndel used hisinvolved croHsse noticed thwaseeds, someen 2 – 1 cs and Statististrian monk, Goredern geneticas.ny experimneknled green seheadd smooth yhealld wrinkleedmged to 6–1 g M ts s. o re tics u m m An A ndation for ne of his that had wri e offspring s, and som ach type se mption e Statis day u O th the fo onastery. s with peas , some of yellow see entages of d on the ass red his d e u To m d is d b at the yellow see larity. That ad wrinkle ts, the perc theory base then cross u h en He smooth d with reg eds, some l experim ted his lt s. ry c c urre re en se se v e ra e l fo rmu la ic t th e re su e if h is theo is o ooth g , after nd d e. Me to pre. lts to se d in th had sm Furthermore ly the sam s and tried generation retical resu is explaine te it t o seeds. approxima cessive tra ver the nex ith the the test, which o w remain inant and re 556 seeds tual results ” chi-square is chapter. cGraw -Hill, d c of dom d examine pared the a d a “simple the end of th rk: M ew Yo n tics (N a s a e co m e u se e d a t Statis pe y, h ,h isit io n to Finall To do this oday—Rev Empiri cal In troduct orrect. ics T b, An was c See Statist hfield, Stat La cha pter. D. Kre., ch, and R. Crutc ission ges, Jr sed with pe rm. The outline and learning objectives are al for : J. Hod Source. 228–229. 1975), pp U dence interv an- r st followed by a feature titled Statistics nd a confi variance o 7 and 8 to hapters othesis ab fi out a single mple Today, in which a real-life problem shows d in C “If a sa h the ch as du c ti o n tribu tion w as use to test a hy on an d p trib utio ns, su lected wit e of be se ependenc students the relevance of the material in Intro are dis ard deviati ncy dis color hi-squ The c nce or stand a erning freque will each test the ind , s conc obile colors n be used to the chapter. This problem is subsequently a vari viation. r te st e used fo f auto dard d an also be a choice o re distribu m tion c a solved near the end of the chapter by It c iven i-squa of b uy ers is g y?” The ch freque nc using the statistical techniques presented same in the chapter. 11–2 xv blu34978_fm.qxd 9/11/08 10:13 AM Page xvi 38 Chapter 2 Freque ncy Distrib utions and Graphs Two typ frequency es of frequen cy structing distribution and distributions tha these dis the grou t are mo tributions ped st are show frequency distri often used are Categor n now. bution. Th the ical Freq e proced categorical The categ uency ures for or Distrib con- gories, su ical frequency utions ch as nomi distribut religious na l- or ordin ion is used fo affiliatio al-lev r data Exampl n, or major el data. Fo that can e 2–1 fie ld of study r ex am be place Distribut would us ple, data such as d in specific cate- e categor ion of Bl ical frequ political affiliatio Twenty- ood Type ency distri n, five arm s butions. data set y inductee Over 300 examples with detailed solutions is A s were giv en a blo od test to determine B serve as models to help students solve O B their blo O AB od type. B B O The B AB O B problems on their own. Examples are solved A A O O O AB O Construct A O AB by using a step by step explanation, and a frequen B cy distri A Solutio bution fo n r the data. illustrations provide a clear display of results Since the A, B, O, data are ca and AB. tegorical, discre for students. The pr These typ te classe es s can be given ne ocedure for cons will be used as used xt. tructing the classe. There are four a frequen s for the blood typ Step 1 cy distri Make a tab bution fo distribution. es: le as show r categor n. ical data A is Class B Tally C A Frequenc D y B Percent O AB Step 2 Tally the Step 3 data and Count the place the results in Step 4 tallies an column B. Find the d pla ce the res percenta ults in co ge of value lumn C. s in each %! f" class by n 100% using the formula where f ! example frequency of the , in the cla cla ss of typ ss and n ! total e A blood %! 5 , the perce number of value 25 " 100% ! 20% ntage is s. For 422 Chapter 8 Hypothesis Testing Percenta be added ge s are since the not normally pa Also, the y rt Using this information, answer these questions. Step 5 decimal are used in certa of a frequency dis equivale in Find the nt of a pe types of graphs tribution, but the tot rcent is ca su y 1. What hypotheses would you use? table is sh als for columns lled a re ch as pie graphs can 2–4 own. C (frequenc lative fre. 2. Is the sample considered small or large? y) and D quency. (percent). 3. What assumption must be met before the hypothesis test can be conducted? The comp leted 4. Which probability distribution would you use? 5. Would you select a one- or two-tailed test? Why? 6. What critical value(s) would you use? 7. Conduct a hypothesis test. Use s ! 30.3. 8. What is your decision? 9. What is your conclusion? 10. Write a brief statement summarizing your conclusion. 11. If you lived in a city whose population was about 50,000, how many automobile thefts per year would you expect to occur? See page 468 and page 469 for the answers. Exercises 8–2 For Exercises 1 through 13, perform each of the businesses in the United States is greater than $24 billion. following steps. A sample of 50 companies is selected, and the revenues (in a. State the hypotheses and identify the claim. billions of dollars) are shown. At a ! 0.05, is there enough evidence to support the researcher’s claim? s ! 28.7. b. Find the critical value(s). 178 122 91 44 35 c. Compute the test value. 61 56 46 20 32 d. Make the decision. 30 28 28 20 27 e. Summarize the results. 29 16 16 19 15 41 38 36 15 25 Use diagrams to show the critical region (or regions), 31 30 19 19 19 and use the traditional method of hypothesis testing 24 16 15 15 19 un