Giáo trình Essentials of statistics 6e by triola

www.ebookslides.com 6th EDITION ESSENTIALS OF STATISTICS www.ebookslides.com www.ebookslides.com 6th EDITION ESSENTIALS OF STATISTICS MARIO F TRIOLA Special Contributions by Laura lossi, Broward College www.ebookslides.com Director, Portfolio Management Deirdre Lynch Senior Portfolio Manager Suzy Bainbridge Content Producer Peggy McMahon Managing Producer Scott Disanno Manager, Courseware QA Mary Durnwald Manager, Content Development Robert Carroll Senior Producer Vicki Dreyfus Product Marketing Manager Emily Ockay Field Marketing Manager Andrew Noble Field Marketing Assistant Erin Rush Senior Author Support/ Technology Specialist Joe Vetere Manager, Rights and Permissions Gina Cheselka Text and Cover Design, Illustrations Production Coordination, Composition Cenveođ Publisher Services Cover Image: â Laura A Watt/Getty Images Copyright © 2019, 2015, 2014 by Pearson Education, Inc All Rights Reserved Printed in the United States of America This publication is protected by copyright, and 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endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner and Pearson Education, Inc or its affiliates, authors, licensees or distributors MICROSOFT AND >OR ITS RESPECTIVE SUPPLIERS MAKE NO REPRESENTATIONS ABOUT THE SUITABILITY OF THE INFORMATION CONTAINED IN THE DOCUMENTS AND RELATED GRAPHICS PUBLISHED AS PART OF THE SERVICES FOR ANY PURPOSE ALL SUCH DOCUMENTS AND RELATED GRAPHICS ARE PROVIDED “AS IS” WITHOUT WARRANTY OF ANY KIND MICROSOFT AND >OR ITS RESPECTIVE SUPPLIERS HEREBY DISCLAIM ALL WARRANTIES AND CONDITIONS WITH REGARD TO THIS INFORMATION, INCLUDING ALL WARRANTIES AND CONDITIONS OF MERCHANTABILITY, WHETHER EXPRESS, IMPLIED OR STATUTORY, FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT IN NO EVENT SHALL MICROSOFT AND >OR ITS RESPECTIVE SUPPLIERS BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF INFORMATION AVAILABLE FROM THE SERVICES THE DOCUMENTS AND RELATED GRAPHICS CONTAINED HEREIN COULD INCLUDE TECHNICAL INACCURACIES OR TYPOGRAPHICAL ERRORS CHANGES ARE PERIODICALLY ADDED TO THE INFORMATION HEREIN MICROSOFT AND >OR ITS RESPECTIVE SUPPLIERS MAY MAKE IMPROVEMENTS AND >OR CHANGES IN THE PRODUCT(S) AND >OR THE PROGRAM(S) DESCRIBED HEREIN AT ANY TIME PARTIAL SCREEN SHOTS MAY BE VIEWED IN FULL WITHIN THE SOFTWARE VERSION SPECIFIED Library of Congress Cataloging-in-Publication Data Names: Triola, Mario F., author | Title: Essentials of statistics / Mario F Triola ; special contributions by Laura Iossi, Broward College Description: 6th edition | New York, New York : Pearson, 2019 | Includes bibliographical references and index Identifiers: LCCN 2017027272| ISBN 9780134685779 (student edition) | ISBN 0134685776 (student edition) | ISBN 9780134687094 (instructor’s edition) | ISBN 0134687094 (instructor’s edition) Subjects: LCSH: Statistics | Mathematical statistics Classification: LCC QA276.12 T776 2017 | DDC 519.5 dc23 LC record available at https://lccn.loc.gov/2017027272 Student Edition ISBN-13: 978-0-13-468577-9 ISBN-10: 0-13-468577-6 www.ebookslides.com To Ginny Marc, Dushana, and Marisa Scott, Anna, Siena, and Kaia www.ebookslides.com ABOUT THE AUTHOR Mario F Triola is a Professor Emeritus of Mathematics at Dutchess Community College, where he has taught statistics for over 30 years Marty is the author of Elementary Statistics, 13th edition, Elementary Statistics Using Excel, 6th edition and Elementary Statistics Using the TI-83>84 Plus Calculator, 5th edition; he is a co-author of Biostatistics for the Biological and Health Sciences, 2nd edition, Statistical Reasoning for Everyday Life, 5th edition, and Business Statistics Elementary Statistics is currently available as an International Edition, and it has been translated into several foreign languages Marty designed the original Statdisk statistical software, and he has written several manuals and workbooks for technology supporting statistics education He has been a speaker at many conferences and colleges Marty’s consulting work includes the design of casino slot machines and fishing rods He has worked with attorneys in determining probabilities in paternity lawsuits, analyzing data in medical malpractice lawsuits, identifying salary inequities based on gender, and analyzing disputed election results He has also used statistical methods in analyzing medical school surveys, and in analyzing survey results for the New York City Transit Authority Marty has testified as an expert witness in the New York State Supreme Court The Text and Academic Authors Association has awarded Marty a “Texty” for Excellence for his work on Elementary Statistics vii www.ebookslides.com CONTENTS INTRODUCTION TO STATISTICS EXPLORING DATA WITH TABLES AND GRAPHS 1-1 1-2 1-3 2-1 2-2 2-3 2-4 Statistical and Critical Thinking Types of Data 13 Collecting Sample Data 25 40 Frequency Distributions for Organizing and Summarizing Data Histograms 51 Graphs That Enlighten and Graphs That Deceive 57 Scatterplots, Correlation, and Regression 67 42 DESCRIBING, EXPLORING, AND COMPARING DATA 3-1 3-2 3-3 Measures of Center 82 Measures of Variation 97 Measures of Relative Standing and Boxplots 112 PROBABILITY 4-1 4-2 4-3 4-4 4-5 131 Basic Concepts of Probability 133 Addition Rule and Multiplication Rule 147 Complements, Conditional Probability, and Bayes’ Theorem Counting 169 Probabilities Through Simulations (download only) 177 159 DISCRETE PROBABILITY DISTRIBUTIONS 5-1 5-2 5-3 Probability Distributions 186 Binomial Probability Distributions Poisson Probability Distributions 184 199 214 NORMAL PROBABILITY DISTRIBUTIONS 6-1 6-2 6-3 6-4 6-5 6-6 226 The Standard Normal Distribution 228 Real Applications of Normal Distributions 242 Sampling Distributions and Estimators 254 The Central Limit Theorem 265 Assessing Normality 275 Normal as Approximation to Binomial 284 ESTIMATING PARAMETERS AND DETERMINING SAMPLE SIZES 7-1 7-2 7-3 7-4 Estimating a Population Proportion 299 Estimating a Population Mean 316 Estimating a Population Standard Deviation or Variance Bootstrapping: Using Technology for Estimates 342 356 Basics of Hypothesis Testing 358 Testing a Claim About a Proportion 373 Testing a Claim About a Mean 387 Testing a Claim About a Standard Deviation or Variance INFERENCES FROM TWO SAMPLES 9-1 9-2 9-3 Two Proportions 416 Two Means: Independent Samples 428 Two Dependent Samples (Matched Pairs) 297 332 HYPOTHESIS TESTING 8-1 8-2 8-3 8-4 80 399 414 442 ix www.ebookslides.com 618 Index of Applications Tornadoes, 49, 56, 66, 94, 110, 282, 396, 397, 575 Weather-Related Deaths, 553 Weighing Seals, 478, 492, 501 Wildlife Population Sizes, 319 Food/Drink Arsenic in Rice, 8, 128, 329, 549 Burger King, 49, 56 Caffeine in Soft Drinks, 93, 108, 330, 349 Cereal, 475 Chocolate, 10, 488, 501–502, 553, 573 Chocolate Chip Cookies, 330, 550, 577 Coffee Vending Machines, 406 Coke and Pepsi, 438 Coke Cans, 274, 397, 405, 406, 552, 576 Cookies, 75, 283 Diet Coke, 438 Diet Pepsi, 282 Dunkin’ Donuts, 47, 282 Fast Food Drive-Thru, 156–157, 406, 407, 424 Fast Food Service Times, 24, 77, 330, 548, 576 Garlic, 329, 340, 397 Healthy Water, 11 Ice Cream, 26 Lemons, 477, 492 McDonald’s, 23, 38, 44, 47, 48, 61, 283, 312, 348 Mercury in Sushi, 329 M&Ms, 24, 212, 254, 311, 314, 384, 521, 576 Pizza, 477, 491, 501 Potatoes, 11 Seafood Consumption, 158 Sugar in Oranges, 320 Wendy’s, 4, 56 Games and Gambling Blackjack, 177 California Daily Lottery, 520 Casino Games, 197 Casino Size and Revenue, 475 Craps, 194 Gambling Win Rates, 141, 154 Kentucky Derby Odds, 146–147, 520 Kentucky Pick 4, 146 Loaded Die, 519 Lottery, 76, 173 Maine Pick 4, 216 Mega Millions, 176 New Jersey Lottery, 143 New Jersey Pick 6, 174 Ohio Pick 4, 198 Oregon Pick 4, 174 Payoff Odds, 142 Pennsylvania Cash 5, 180 Powerball, 175, 220 Roulette Odds, 146–147, 194, 199 Shuffling a Deck of Cards, 170 Slot Machines, 519 South Carolina Pick 3, 222 Virginia Pick 3, 198 Wild Card Lottery, 180 Winning the Lottery, 137 General Interest Aluminum Cans, 577 Area Codes, 175 Astrology, 315, 367 ATM Pin Numbers, 174 Atomic Clock, 462 Bathtubs, 43 Belief in the Devil, 2–4 Biometric Security, 292, 383 Brain Volume and IQ, 74 Celebrities and the Law, 350 Celebrity Net Worth, 92, 108, 330 Challenging Intuition, 135 Coin Toss, 187, 192–193 Color and Cognition, 439 Color and Creativity, 438 Combination Locks, 174 Crowd Size, 322 Diamond Rings, 93, 109 Dictionary, 33 Dreaming in Black and White, 425 English Words, 397 ESP, 381, 413 Ethics, 65 Eye Contact, 252 Flirting, 196 Friday the 13th, 451 Fuzzy Central Limit Theorem, 269 Garbage, 283, 475, 578 Gender Gap in Drug Testing, 446 Guessing Birthdays, 144 Housing Units, 23 Human Lie Detectors, 392 Identity Theft, 176 Journal Retractions, 65 Las Vegas, 92, 108 Lead and IQ, 126, 547, 548 Length of One Minute, 398 Loch Ness Monster, 385 LOL, 156 Lost Wallet Experiment, 528 Measurement of Time, 98 Mint Specs, 407 Misleading Statistics in Journalism, 16 Monty Hall Problem, 183 Morse Code, 176 Moving Companies, 175 Newspapers, 351 News Sources, 209 Nobel Laureates, 470, 476–477, 491, 493, 501–502, 573 Online Dating, 20 Online News, 351 Palm Reading, 471 Paying for First Dates, 35 Periodic Table, 23 Personal Security Codes, 172 Pickup Lines, 196 Planets, 221 Postponing Death, 484 Quarters, 252, 341, 440 Radioactive Decay, 219 Random Secretary, 169 Reaction Time, 507 Real Estate Agents, 427 Reincarnation, 210 Safe Load of Elevators, 268, 272–273 Sexuality of Women, 33 Shakespeare’s Vocabulary, 302 Shared Birthdays, 168 Six Degrees of Separation, 18 Sleepwalking, 143, 150, 198, 290, 378 Social Security Numbers, 24, 174 Speed Dating, 93, 109, 126, 329, 348, 450, 549, 553, 573 Spoken Word, 450 Tattoos, 211 Testing Laboratory Gloves, 423 Thanksgiving Day, 139–140 Time and Motion, 504 Twins in Twinsburg, 445 UFO Poll, 33 Washing Hands, 223 Words Spoken in a Day, 406, 493, 575 World Records, 87 Wristwatch Accuracy, 352, 413 Yawning, 428, 529 ZIP Code, 175 Health and Medicine Acupuncture, 33 Adverse Drug Reactions, 383 Anemia, 212 Aspirin, 212, 367, 371, 427 Atkins Weight Loss Program, 34, 329, 340 Baby Weights, 113 Back Pain Treatment, 32 Biomedical Journals, 65 Birth Weight, 23, 35, 94, 110, 125, 127, 250, 320, 328, 406, 442, 548 Blood Platelet Counts, 55 Blood Pressure, 34, 94, 109, 498 BMI, 126, 439 Body Temperatures, 11, 24, 37, 64, 76, 94, 110, 253, 270, 328, 331–332, 391–392, 396, 406, 450, 568 Bone Density Test, 232–237, 241–242, 291–292 California Health Interview Survey, 23 Cardiac Arrest, 425 Carpal Tunnel Syndrome, 424 Chantix, 373 Chickenpox, 314 Cholesterol, 329, 340, 397 Cigarette Contents, 572 Cigarette Tar, 503 Clinical Trials, 10, 19, 26, 176, 209, 370, 527 Coffee and Memory, 146 www.ebookslides.com Index of Applications Cost of Giving Birth, 66 Defective Pacemakers, 158 Diabetes, 179 Diastolic Blood Pressure, 50, 65, 291–292, 398 Diet and Exercise Programs, 10 Diet Pills, 432 Discharges After Birth, 521 Disease Clusters, 219 Drug Approval, 370 Duragesic, 506 Duration of Pregnancy, 253 Echinacea, 426 Effects of Alcohol, 442 Eliquis, 38, 348 Emergency Room Visits from Sports Injuries, 44 Experiment Design, 176 Female Pulse Rate, 248 Foot Lengths, 93 Framingham Heart Study, 34 Freshman 15, 23 Gender Selection, 7, 10, 23, 134, 138, 143, 205, 289, 313, 373, 412 Growth Charts, 46 Handwashing, Hawthorne and Experimenter Effects, 27 Headache Treatment, 426 Health Test, 76 Heart Failure, 201 Heart Health Study, 34 Height and Shoe Lengths, 70 Heights of Fathers and Sons, 70 Hemoglobin, 437–438 Hip Protectors, 530 HIV Infection, 212 HIV Vaccine, 34 Hospital Generators, 158 Hospitals, 35 Hypnotism for Reducing Pain, 451 Insomnia Treatment, 329, 340, 398 IQ and Lead Exposure, 440 Lead in Blood, 24 Lead in Medicine, 398 Lipitor Test, 33, 34, 58, 313, 552 Low Birth Weight, 252 Lunesta, 34 Magnet Treatment of Pain, 439 Malaria, 426 Male Pulse Rates, 253 Marijuana Study, 34 MCAT, 10 Medical Helicopters, 158 Medical Malpractice, 312, 349, 384 Medication Usage, 313, 386 Nicotine Patch Therapy, 306, 385 Nurses’ Health Study, 34 Online Medical Info, Organ Donors, 180 OxyContin, 312, 384, 425 Penicillin, 143 Pharmaceutical Research and Manufacturers of America, 34 Physician’s Committee for Responsible Medicine, Physician’s Health Study, 33, 35 Platelet Counts, 114 Polio Experiment, 420 Pulse Rates, 65, 94, 110, 330, 331–332, 371, 398, 405, 548 Pulse Rates of Males, 58 Red Blood Cell Counts, 125, 409 Salk Vaccine Experiment, 25, 411 Second-Hand Smoke, 322 Six Children, 37 Sleep, 127, 388–391 Smokers, 11, 63, 93, 109, 532 Smoking and Cancer, 498 Smoking Cessation, 314, 385, 424 Splint, 532 Syphilis, 162 Systolic Blood Pressure, 50 Tooth Fillings, 552 Touch Therapy, 313, 384, 385 Transportation in Serious Injuries, 427 Vision Correction, 179, 210 Vitamin C, 371 Waist and Arm Circumferences, 68, 69 Weight and Pulse Rate, 68, 69 West Nile Vaccine, 34 Law and Crime Author as a Witness, 421 Bias in Jury Selection, 386 Crime Witnesses, 160 CSI Statistics, 477, 479, 492, 493 Detecting Fraud, 221 Eyewitness Accuracy, 454 Identification of Thieves, 435 Licence Plate Laws, 424 Lie Detectors, 379, 384, 532 Police Calls, 520 Prosecutor’s Fallacy, 161 Serial Killers, 534 Ticketing Out-of-Towners, 466 Military Air Force Height Requirement, 244 Air Force Pilots, 251 Loading Aircraft, 275 Navy Pilots, 251 Survivorship Bias, Tank Serial Numbers, 321 People and Psychology Ages of Children, 258 Arm Circumferences, 283 Basic and Applied Social Psychology, 364 Birth Rate in China, 166 Birth Rate in United States, 166 Birth Rates, 262, 569 BMI for Miss America, 409 Body Data, 568 Brain Sizes, 9–10 Brain Volumes, 283, 339, 451 Eye Color Survey, 344 Family Heights, 569 Florence Nightingale, 59 Foot and Height, 568 Foot Lengths of Women, 295 Gender Selection, 211 Heights, 124, 454 Heights of Fathers and Sons, 450 Heights of Males, 55, 451 Heights of Mothers and Daughters, 450 Heights of Presidents, 451 Heights of Supermodels, 398, 401, 403 How Many People Do You Know?, 343 Humans Born Throughout History, 545 IQ and Brain Volume, 502, 570 IQ and Lead Exposure, 440, 570 IQ Scores, 10 Justin Gaitlin, 87 Katy Perry, 138 Last Digits of Weights, 521 Left-Handed People, 314, 351, 427 Left-Handed People’s Life Spans, 237 Mean Height of Men, 371 Measuring Disobedience, 17 Polls and Psychologists, 525 Publication Bias, Stephen Jay Gould, 84 Tallest and Shortest Men, 125 Tallest Person, 37 Variation in Faces, 102 Weights of Californians, 513 Politics and Government Age of Presidents, 282 Defense of Marriage Act, 36 Election Ballots, 409 Exit Poll, 24, 33 Federalist Papers, 44 House Attendance, 23 Lying Voters, 290 NSA, 19 POTUS, 478, 493 Presidential Elections, 212 President Life Spans, 95 Presidents, 572 Push Polling, 300 Single Vote Determining an Election, 164 Surveying Senators, 209 United Nations headquarters, Voting Ballots, 212 World War II Bombs, 219, 520 Social Issues Alcohol and Tobacco in Movies, 571 Composite Drug Test, 168 Composite Water Samples, 168 619 www.ebookslides.com 620 Index of Applications Crime Research, 34 Criminal Forensics, 24 Divorce, 36 Drug Screening, 151, 152 Firefighter Fatalities, 93, 108 Marijuana Use, 157 Murders, 219 Parking Meter Theft, 94, 109 Passive and Active Smoke, 571 Police Deaths in Car Chases, 72 Secondhand Smoke, 550 Phone Surveys, 166 Poll Samples, 156 Polls and Psychologists, 525 Security Survey, 221 Stem Cell Survey, 384 Survey Pitfalls, 31 Survey Refusals, 535 Survey Reliability, 175 Survey Return Rates, 312, 349, 384 UFO Poll, 33 Technology and Internet Sports Ball Sizes, 479, 493 Baseball, 24, 521, 535 Batting Averages, 100 Denver Bronco Salaries, 328 Emergency Room Visits from Sports Injuries, 44 Football Player Numbers, 92, 107 Football Player Weights, 92, 107 Golf Tees, 175 Home Field Advantage, 535 Home Runs, 65 Horse Races, 171, 180 Miami Heat Salaries, 328 NFL, 466 NY Knicks Salaries, 294 Overtime in Football, 203, 385 Soccer Shootout, 174, 534 Super Bowl, 24, 385, 433 Swimming Accidents, Tennis Challenge, 222, 424, 533 Tennis Instant Replay, 384 Triathlon Times, 549 World Series Games, 521 Surveys and Opinion Polls AARP Survey, 35 Bias in Internet Surveys, 304 California Health Interview Survey, 23 Class Surveys, 33 Curbstoning, 308 Eye Color Survey, 344 Harris Interactive Survey, 22 Health Survey, 23 Lead Margin of Error, 418 Literary Digest Poll, 33 Meta-Analysis, 190 Nonvoters, 313 Not at Home, 189 AAA Batteries, 212 Airbus 310, 154 Benford’s Law, 515–516 Biometric Security, 221 Cell Phone Ownership, 383 Cell Phone Radiation, 92, 108, 126, 348 Cell Phones and Cancer, 146, 291, 313 Cell Phones and Driving, 505 Cell Phones and Handedness, 426 Cell Phone Use, 197, 371, 532 Comparing Data Speeds, 120 Computer Hard Drives, 157–158, 168 Computers, 76, 351 Cybersecurity, 519 Data Speeds, 124, 327 Defective iPhones, 166 Drone Delivery, 208, 358, 375 Electricity, 175 Internet and Nobel Laureates, 476–477 iPads, 160 Online Data, 371 Smartphone Usage, 10, 24, 290 Stadium Generators, 168 Telephones, 43 Verizon Data Speeds, 91, 101, 106, 119 Wi-Fi, 166 Transportation and Travel Aircraft Altimeters, 406 Aircraft Cockpit Design, 246 Aircraft Seat Design, 125 Airline Seatings, 315 Airport Data Speeds, 83, 396, 578 Airport Security, 229 American Airlines, 353 Black Cars, 179 Boat Thefts, 59–60 Boeing 767-300, 291 Braking Reaction Times, 455–456 Car and Taxi Ages, 441 Car Booster Seats, 398 Car Crashes, 477, 492, 574 Car Fatalities, 219 Car License Plates, 535 Car Measurements, 574 Car Repair Costs, 554 Car Rollovers, 145 Car Seat Safety, 515 Car Weight and Fuel Consumption, 75 Cell Phones and Driving, 505 Commercial Flights, 156 Corvettes, 23 Drinking and Driving, 33 Driver Aggression, 34 Effectivity of Seat Belts, 425 Ejection Seat Design, 274 Executive Jet Doorway, 252 Fatal Drunk Driving, 180 Federal Aviation Administration, 138 FedEx Deliveries, 175 Flight Costs, 455 Flight Delays, 549 Helicopters, 427 Highway Strength, 33 Independent Jet Engines, 152 Jet Ejection Seats, 252 Luggage, 143 Motorcycle Helmets, 535 Motor Vehicle Fatalities, 552 On-time Arrivals, 353 On-time Flights, 23 Overbooking Flights, 223 Probability of Car Colors, 289 Revised mpg Ratings, 477, 492 Safest Seats in a Commercial Jet, 528 Seatbelts, 76, 146, 178, 440 Seating Choice, 347 Self-Driving Vehicles, 66, 196, 383 Sobriety Checkpoints, 156 Southwest Airline Seats, 274 Subway Fare, 66, 477, 491, 501 Taxi Cabs, 238 Texting and Driving, 139, 533 Texting Fatalities, 24 Titanic, 23 Tour Boats, 274 Travel Itinerary, 170 Water Taxi Safety, 253, 273 www.ebookslides.com INDEX A Acceptance sampling, 158 Actual odds against, 142 Actual odds in favor, 142 Addition rule complementary events and, 149–150 complements and, 159 defining, 148 disjoint events and, 149 formal, 148 intuitive, 148 notation for, 148–149 summary of, 155–156 Airport data speeds, 578 Alcohol and tobacco in movies, 571 a, 238, 300 Alternative hypothesis, 470 contingency tables, 523 defining, 359 goodness-of-fit and, 511 original claim for, 359–360 Aluminum cans, 577 Analysis of data, potential pitfalls, 7–8 Analysis of variance (ANOVA), 540 See also One-way ANOVA Area between boundaries, 232 known, 236–239, 245–248 with nonstandard normal distribution, 243 probability and, 229, 232 z scores and, 231, 232, 235 Arithmetic Mean See Mean Aspirin, 367 Average, 83 B b1 slope, 73, 480, 481 Bar graphs, 59 Bayes’ theorem, 163–165 Bear measurements, 570 bell-shaped distribution, 228 b, 228 Benford’s law, 509, 515–516 Bias in internet surveys, 304 in missing data, 22 publication, Biased estimators, 99, 106–107, 261 Big data, 14, 19 applications of, 20–21 Bimodal, 85 Binomial probabilities, 559 technology for, 288 Binomial probability distribution, 199–205 defining, 200 finding, 201–204 formula, 202 normal distribution approximation of, 285 notation, 200, 284 rationale for, 207–208 software/calculator results, 208 Births, 569 Bivariate normal distribution, 463 Blinding, 26 Blocks, 30–31 Body data, 568 Body temperatures, 568 Bonferroni multiple comparison test critical values in, 544 one-way ANOVA, 544–546, 550 P-values in, 544 Bootstrap resampling for claims testing, 393 for dependent samples, 447 for matched pairs, 447 Bootstrap sample for confidence interval, 343–344 defining, 343 means and, 345 proportions and, 344 requirements, 342 standard deviation and, 346 Box, George E P., 537 Boxplots, 112–120 constructing, 119–120 defining, 119 for mean, 543 modified, 121–122 skeletal, 121 skewness in, 119 C Calculators See Software/calculator results Cancer, 498 Car chases, 72 Car crash tests, 573 Car measurements, 573 Car seats, 515 Case-control study, 29 Categorical data, 14–15 in frequency distributions, 44–45 Causation correlation and, 7, 68, 469 interpretation with, 469 Censored data, 95 Census, Central limit theorem, 265 applications of, 268–270 defining, 266 fuzzy, 269 sample mean and, 267 sampling distribution and, 267 universal truths and, 266–267 Chebyshev’s theorem, 105 Chi-square distribution, 333–335, 571 critical values in, 333 degrees of freedom in, 333 properties of, 400 Chi-square test of homogeneity, 528 Chocolate chip cookies, 577 Cigarette contents, 572 Claimed distribution disagreement with, 512–513 in goodness-of-fit, 512–513 Claims testing with abnormal populations, 403 bootstrap resampling for, 393 confidence interval for, 377–378, 391–392, 402–403 critical values for, 377, 391 critical values in, 402 degrees of freedom in, 400 equivalent methods, 400 exact methods, 379–383 important properties of, 388 normal approximation method, 374–379 notation, 387 number of successes, 377–378 about population means, 387–395 about population proportion, 374–383 P-value in, 375–376, 388–390 requirements, 387, 399 sign test for, 393 about standard deviation, 399–404 technology for, 388–389 test statistic, 387, 394, 399 about variance, 399–404 Wilcoxon signed-ranks test for, 393 Class boundaries, 42, 43 midpoints, 42 size, 83 width, 42, 43 CLI See Cost of laughing index Clinical trials, 14 alternatives to, 527 observational studies compared with, 26 Clopper-Pearson method, 309–310 Cluster sampling, 28 Coefficient confidence, 300 linear correlation, 70, 463–466 Pearson correlation, 564 Pearson product moment correlation, 463 Spearman’s rank correlation, 565 of variation, 106 Coefficient of variation (CV) defining, 106 round-off rule for, 106 Cohort study, 29 Coincidences, 165 Coin weights, 577 Cola weights, 576 Combinations defining, 170 mnemonics for, 170 permutations and, 173–174 rule, 172 Commercial jet safety, 528 Complementary event addition rule and, 149–150 defining, 140 probability and, 140–141 rule of, 150 Complements addition rule and, 159 multiplication rule of, 156 probability and, 159–160 Completely randomized design, 30, 543 Composite sampling, 168, 179 621 www.ebookslides.com 622 Index Conclusions, misleading, Conditional probability, 161–163 defining, 161 formal approach for, 161 intuitive approach for, 161 notation, 161 Confidence coefficient, 300 Confidence interval analyzing polls, 305–306 better-performing, 309 bootstrap sample for, 343–344 for claims testing, 377–378, 391–392, 402–403 Clopper-Pearson method, 309–310 for comparisons, 336 constructing, 304, 335–336 critical values, 301–302 data comparisons with, 322–323 defining, 300 as equivalent method, 444 for hypothesis tests, 306–307, 336, 367 in independent samples, 433–434 interpreting, 301, 321–322 manual calculation, 305 margin of error and, 322, 434–435 for matched pairs, 443–444 for mean, 543 notation, 303 one-sided, 316 plus four method, 309 point estimate and, 306, 322 for population mean, 317 for population proportion, 303–304 for population standard deviation, 335 population variance, 335 procedure for, 319 rationale for, 337–338, 421–422 requirement check, 303, 304 round-off rule, 303 software/calculator results, 338, 422 technology and, 304–305 for two dependent samples, 443–444 in two proportions, 416, 420–421 Wald, 309 Wilson score, 309–310 Confidence level defining, 300 process success rate, 301 Confounding, 29 Confusion of the inverse, 163 Constitution, 44 Context, 3–5 Contingency tables alternative hypothesis, 523 basic concepts, 522–527 critical thinking, 532–536 critical values in, 524 defining, 523 degrees of freedom in, 524 expected frequencies in, 524 expected value in, 525 notation, 523 null hypothesis, 523 observed frequencies in, 524 P-values in, 523 requirements, 523 software/calculator results, 531 test statistic in, 523 Continuity correction defining, 287 uses of, 287–288 Continuous data, 15–16 Continuous random variable, 187 Convenience sampling, 28 Convictions, 160 Correlation, 67–74 basic concepts of, 461 causation and, 7, 68, 469 common errors involving, 469–470 defining, 68, 461 determining, 70 formal hypothesis test and, 470–472 linear, 68, 71–72, 461–464, 467–469 negative, 462 nonlinear relationship in, 470 positive, 462 regression and, 484 software/calculator results for, 472–473 Cost of laughing index (CLI), 15 Course evaluations, 573 Critical region, 363 Critical thinking contingency tables, 532–536 goodness-of-fit and, 519–522 one-way ANOVA, 546–550 standard deviation for, 205–208 Critical values in Bonferroni multiple comparison test, 544 in chi-square distribution, 333 for claims testing, 365, 377, 391, 402 confidence interval, 301–302 in contingency tables, 524 decision criteria for, 366 defining, 238, 302 finding, 318 for goodness-of-fit, 511 in hypothesis testing, 362, 365 in independent samples, 432–433 in one-way ANOVA, 542 in population means, 318 rank correlation, 494–499 in two proportions, 417, 419–420 Cross-sectional study, 29 Crowd size, 322 Cumbersome calculations, 152 Cumulative frequency distribution, 45 Curbstoning, 308 CV See Coefficient of variation D Data analysis of, basic types of, 13–22 big, 14, 19–21 body, 568 categorical, 14, 44–45 center of, 51 confidence intervals, 322–323 continuous, 15–16 defining, discrete, 15–16 distribution of, 51 falsification of, 517 magnitude in sets of, 20 missing, 21–22 quantitative, 14 science, 20–21 sources of, 3, spread of, 51 Data transformation, 280 Death, 484 Decimals, Degree of confidence, 300 Degrees of freedom (df ) in chi-square distribution, 333 in claims testing, 400 in contingency tables, 524 in independent samples, 430 in population means, 318 two means and, 430 Denomination effect, 167, 426 Density curve, 229 Dependence, 151 independence and, 201 Dependent samples bootstrap resampling for, 447 confidence interval for, 443–444 equivalent methods for, 444 experimental design for, 442–443 hypothesis test for, 443 notation for, 443 software/calculator results for, 447–448 technology and, 446 test statistics for, 443 Dependent variable, 480 df See Degrees of freedom Descriptive statistics, 81 Diet pills, 432 Discordant categories, 529–530 Discrete data, 15 finite type, 16 infinite type, 16 Discrete random variable, 187 Disjoint events, 149 Disobedience, 17 Dispersion See Variation Distance, 231 Distribution See specific types Distribution-free method, 342 Dotplot, 57 Double-blind, 26 Driving tickets, 466 Drug approval, 370 Duncan test, 544 E Earthquakes, 573 Empirical rule, 104–105 Enumeration district, 28 Equally likely, 512 Error See Margin of error Estimators biased, 99, 106–107, 261 defining, 261 unbiased, 103, 106–107, 261, 263, 299–300 Events complementary, 140–141, 149–150 defining, 134 disjoint, 149 probability of, 135–140 rare, 141–142, 192–193, 270 sequential, 165 simple, 134 Exact methods claims testing, 379–383 improving, 381 simple continuity correction, 381 Excel See Software/calculator results Exclusive or, 159 www.ebookslides.com Index Expected frequencies in contingency tables, 524 equal, 512 finding, 512 in goodness-of-fit, 512 rationale for, 527 Expected value, 190–191 in contingency tables, 525 defining, 190 rationale for formulas, 194–195 Experimental units, 26 Experiment design, 25–28 advanced, 29–31 blinding in, 26 completely randomized, 30, 543 defining, 26 for dependent samples, 442–443 hypothesis testing and, 370 matched pairs, 31 for matched pairs, 442–443 one-way ANOVA and, 543 randomization in, 26 replication in, 26 rigorously controlled, 31 Experimenter effects, 27 Explanatory variable, 480 Extrapolation, 484 F Factorial rule defining, 169 notation, 169 False positive/negative, 132 Falsified data, 517 Family heights, 569 Fast food, 576 F distribution, one-way ANOVA, 536–537 Fewer, 16 Finite population, 271 Fisher, R A., 540 Fisher’s exact test, 529 Fitted line plot, 472 5-number summary defining, 118 finding, 118–119 Fluoride, 444 Foot and height, 568 Formal addition rule, 148 Formal hypothesis test, 470–472 Formal multiplication rule, 150 Fractiles, 114 Fractions, Frequency defining, 42 expected, 512, 524, 527 observed, 524 Frequency distribution, 44–45 cumulative, 45 defining, 42 last digits in, 46 mean calculated from, 88–89 normal, 46 procedure for constructing, 43–45 relative, 45 Frequency polygon, 61–62 Freshman 15, 569 Fuzzy central limit theorem, 269 G Gambling, 153 Garbage weight, 578 Gender gap, 446 Geometric distribution, 213 Geometric mean, 96 Global temperatures, 346 Goodness-of-fit alternative hypothesis and, 511 Benford’s law and, 515–516 claimed distribution in, 512–513 critical thinking and, 519–522 critical values for, 511 defining, 511 expected frequencies in, 512 notation, 511 null hypothesis and, 511 P-values for, 511 requirement check, 514 requirements, 511 software/calculator results, 518 testing for, 511 test statistic for, 511, 517 Gosset, William, 318 Gould, Stephen Jay, 84 Graphs bar, 59 deceptive, 62–63 enlightening, 57–62 frequency polygon, 61–62 with nonzero vertical axis, 62–63 Pareto charts, 59–60 pictographs, 63–64 pie charts, 60–61 regression line, 483 software/calculator results, 64 time-series, 58 Graunt, John, Group testing, 162 Growth charts, 46 H Hamilton, Alexander, 44 Harmonic mean, 96 Hawthorne effect, 27 Histograms, 255, 280 basic concepts of, 51–55 defining, 51 distribution shapes, 52 important uses of, 51 interpreting, 52 normal distribution, 52–53, 276 normal quantile plots and, 276–277 probability, 188–189 relative frequency, 51–52 skewness of, 277 uniform distribution, 53 Homogeneity, test of, 527–529 chi-square, 528 procedure, 528 Horvitz, Eric, 18 Hybridization, 224, 265 Hypergeometric distribution, 214 Hypothesis, 358 alternative, 359–360, 470, 511, 523 null, 359–360, 470, 511, 523 Hypothesis testing, 270–271 See also Test statistic basic concepts of, 358–367 big picture, 358–359 confidence intervals for, 306–307, 336, 367 correlation and, 470–472 critical region in, 363 critical values in, 362, 365 defining, 358 for dependent samples, 443 as equivalent method, 444 experiment design and, 370 final conclusion, 366 formal, 470–472 for independent samples, 430 for matched pairs, 443 for means, 429 memory hints for, 367 multiple negatives in, 366 one-tailed, 471 for proportions, 416, 417 P-value in, 363–364 rare event rule and, 270 rationale for, 421 rejection in, 365–366 restating, 366–367 sampling distributions in, 362 for significance, 359 significance level and, 361–362 software/calculator results, 381, 395, 404, 422 test statistic in, 362, 470 type I errors, 367–369 type II errors, 367–369 623 I Identity theft, 435 Inclusive or, 148 Independence dependence and, 201 key components in test of, 524 multiplication rule and, 151–154 testing for, 522–527 test statistic for tests of, 523 Independent events, 151 Independent samples, 428–437 alternative methods, 434–435 confidence interval in, 433–434 critical values in, 432–433 degrees of freedom in, 430 hypothesis testing for, 430 notation, 430 P-values in, 431 requirements, 430 software/calculator results for, 435–436 standard deviation for, 435 Independent variable, 480 Inferences about matched pairs, 443 software/calculator results, 422 about two means, 430 about two proportions, 416 Influential points, 485 Inferential statistics, 141–142 rare event rule for, 192–193 Interquartile range, 118 Interval, 300 level, 18 Interval estimate See Confidence interval Intuitive addition rule, 148 Intuitive multiplication rule, 150 IQ brain size and, 570 lead and, 570 J Jay, John, 44 Jet engine problems, 152 Jobs, 20 K Known area, 236–239, 245–248 L Law of large numbers, 137 Lead margin of error, 418 Least squares property, 487 Left-handedness, 237 Left-tailed test, 363 Less, 16 Lie detectors, 379, 392 www.ebookslides.com 624 Index Linear correlation, 461 defining, 68, 461 determining, 71–72 finding, 467–468 P-values for, 71–72, 497 strength of, 462–464 variation in, 468–469 Linear correlation coefficient, 70 calculation of, 463–466 defining, 463 formulas, 464 interpreting, 464 notation, 463 properties of, 464–465 P-values for, 464 requirements, 463–464 rounding, 464 Loaded questions, Lognormal distribution, 280, 283 Longitudinal study, 29 Lottery, 165, 173 Lower class limits, 42 Lurking variables, 26, 469 M MAD See Mean absolute deviation Madison, James, 44 Magnitudes, 17 Manatee deaths, 571 Manual construction, 277–280 Margin of error confidence interval and, 322, 434–435 defining, 303 lead, 418 Matched pairs bootstrap resampling for, 447 confidence interval for, 443–444 equivalent methods for, 444 hypothesis test for, 443 inferences about, 443 McNemar’s test for, 529–531 notation for, 443 requirements, 443 software/calculator results for, 447–448 test statistic for, 443 Matched pairs design, 31 experimental, 442–443 McNemar’s test for matched pairs, 529–531 Mean absolute deviation (MAD), 103, 265 Means, 428–437 See also Population mean alternative methods of finding, 434–435 bootstrap sample and, 345 boxplots for, 543 calculation of, 83 calculation of, from frequency distribution, 88–89 confidence interval estimates for, 543 defining, 82 degrees of freedom and, 430 geometric, 96 harmonic, 96 hypothesis testing in, 429 identifying different, 541–546 inferences about, 430 informal methods of comparing, 543 notation, 83 for Poisson probability distribution, 215 of probability distribution, 189 properties of, 82–83 quadratic, 96 sampling distributions and, 255 software/calculator results for, 326, 395, 435–436 standard deviation for, 435 standard error of, 267 test statistics effected by, 541, 542 two, 428–437 weighted, 89–90 Measurement interval level, 18 levels of, 16–19 nominal level, 17 ordinal level, 17 ratio level, 18 units of, 14–15 Measures of center See also specific types advanced concepts, 88–91 basic concepts, 82–88 critical thinking and, 87–88 defining, 82 rounding, 86–87 software/calculator results, 90–91 Median calculation of, 84 class, 96 defining, 84 notation of, 84 properties of, 84 Mendel, Gregor, 224, 285–286, 288, 517 Meta-analysis, 190 Midquartile, 118 Midrange defining, 86 properties of, 86 Milgram, Stanley, 17–18 Minitab See Software/calculator results Misleading conclusions, Misleading statistics, 16 Missing data, 21–22 bias in, 22 completely at random, 21 correcting, 22 not at random, 21–22 M&M weights, 576 Mode defining, 85 important properties of, 85 Modified boxplots constructing, 121–122 outliers and, 121–122 Monte Carlo method, 422 Multimodal, 85 Multinomial distribution, 214 Multiple comparison tests, 543 Multiplication counting rule, 169 Multiplication rule of complements, 156 formal, 150 independence and, 151–154 intuitive, 150 notation for, 150–151 rationale for, 155 redundancy and, 154 summary of, 155–156 Multistage sampling, 28–29 N Negatively skewed, 53 Negative predictive value, 132 Nielsen ratings, 117 Nightingale, Florence, 59 Nobel laureates, 573 Nominal level, 17 Nonlinear patterns, 498–499 Nonlinear relationship, 462 in correlation, 470 Nonparametric method, 342 Nonrandom sampling error, 31 Nonresponse, Nonsampling error, 31 Nonstandard normal distribution, 243 Nonzero vertical axis, 62–63 Normal approximation, 284–285 Normal distribution, 46 advanced methods, 277 binomial distribution approximated with, 285 conversions of, 243 defining, 228 formulas for, 228–229, 232, 242 of normal quantile plots, 276, 277 of outliers, 276 populations with, 276 significance and, 247–248 skewness and, 277 software/calculator results, 249 standard, 230–231 values from known areas, 245–248 Normal distribution histograms, 52–53, 276 Normality assessing, 275–277, 279 assessment of, with normal quantile plots, 53–55 claims testing and, 388 histogram and, 280 normal quantile plots and, 280 outliers and, 280 for population means, 318 Normality assessment, 279 Normal probability plot See Normal quantile plots Normal quantile plots assessing normality with, 53–55 defining, 276 histograms and, 276–277 manual construction of, 277–280 normal distribution of, 276, 277 normality and, 280 software/calculator results, 280 Not equally likely, 512 Null hypothesis, 470 contingency tables, 523 defining, 359 goodness-of-fit and, 511 original claim for, 359–360 Numerical random variable, 187 O Observational studies case-control, 29 clinical trials compared with, 26 cohort, 29 cross-sectional, 29 longitudinal, 29 prospective, 29 retrospective, 29 types of, 29 Observed frequencies, 524 Odds, 141 actual, against, 142 actual, in favor, 142 payoff, 142 Old faithful, 575 One-sided confidence interval, 316 www.ebookslides.com Index One-tailed test, 471 One-way ANOVA, 536–558 basics of, 537–540 Bonferroni multiple comparison test, 544–546 completely randomized design, 543 critical thinking, 546–550 critical values in, 542 defining, 537 experiment design and, 543 fail to reject, 537 F distribution, 536–537 multiple comparison tests and, 543 procedure for, 537 P-value, 537 range tests and, 543 reject, 537 requirements, 537 rigorously controlled design in, 543 software/calculator results, 546 for testing population means, 537 test statistic in, 540–541 Online dating, 20 Orange sugar content, 320 Order of questions, Ordinal level, 17 Oscar winner age, 572 Outliers, 51, 120 modified boxplots and, 121–122 normal distribution of, 276 normality and, 280 software/calculator results, 123 Out-of-town drivers, 466 P Palm reading, 471 Parameters, 13 Pareto charts, 59–60 Passive and active smoke, 571 Payoff odds, 142 Pearson correlation coefficient, 564 Pearson product moment correlation coefficient, 463 Percentages conversion to, from fractions, conversion to decimals, probabilities as, 137 Percentiles, 112–120, 247 conversion of, 116–117 defining, 115 finding, 115 Permutations combinations and, 173–174 defining, 170 mnemonics for, 170 Permutations rule with different items, 171 with some identical items, 171–172 Personal security codes, 172 Pi, 513 Pictographs, 63–64 Pie charts, 60–61 Placebo effect, 26 Plus four method, 309 Point estimate, 299–300 confidence interval and, 306, 322 defining, 299 population mean, 317–318 sample proportion as, 299 Poisson probability distribution, 214 as approximation to binomial, 215–216 formula, 215 mean for, 215 parameters of, 215 properties of, 215 requirements, 215 software/calculator results, 217 Polio experiment, 420 Polls, 525 Pooled estimate, 434 Pooled sample proportion, 416 Pooling, 434 Population abnormal, 403 defining, finite, 271 with normal distribution, 276 standard deviation of, 102 variance of, 102–103 Population mean appropriate distribution for, 325–326 claims testing about, 387–395 confidence interval, 317 critical values in, 318 degrees of freedom in, 318 with known variables, 325–326 normality for, 318 notation, 317 one-way ANOVA for, 537 point estimate, 317–318 requirements, 317 round-off rule, 317 sample size and, 323–324 student t distribution, 318–319 with unknown variables, 317–325 Population proportion claims testing about, 374–383 confidence interval for, 303–304 sample size and, 307–308 Population size, 306 determining, 323–324 role of, 308 Population standard deviation, 332–339 confidence interval for, 335 notation, 335 requirements, 335 round-off rule, 335 Population variance, 332–339 confidence interval, 335 notation, 335 requirements, 335 Positively skewed, 53 Positive predictive value, 132 Posterior probability, 165 Power of hypothesis test, 369 Practical significance, Predictor variable, 480 Presidents, 572 Prevalence, 132 Primary sampling units (PSUs), 28 Prior probability, 165 Probabilistic models, 480 Probability, 233 area and, 229, 232 basic concepts of, 133–141 binomial, 288, 559 classical approach to, 136 complementary events and, 140–141 complements and, 159–160 conditional, 161–163 convictions and, 160 of events, 135–140 finding values from, 246 intuition and, 135 notation for, 135 as percentages, 137 posterior, 165 prior, 165 relative frequency approximation of, 135 significant results and, 270 simulations, 137 in statistics, 133–134 subjective, 136 with z scores, 231–232 Probability distribution basic concepts of, 186–193 binomial, 199–205 defining, 186 mean of, 189 parameters of, 189 Poisson, 214–217 requirements, 187–188 625 round-off rule for, 189 standard deviation for, 189 variance for, 189 Probability formula, 188 Probability histogram, 188–189 Proportion bootstrap sample and, 344 confidence interval in, 416, 420–421 critical values in, 417, 419–420 hypothesis testing in, 416, 417 inferences, 416 notation for, 256, 416 pooled sample, 416 population, 303–304, 307–308, 374–383 P-value in, 417–418 requirements, 416 rounding, 417 sampling distributions and, 255 software/calculator results for, 310, 381, 422 technology and, 419 two, 416–423 Prosecutors’ fallacy, 161 Prospective study, 29 PSUs See Primary sampling units Psychologists, 525 Publication bias, Push polling, 300 P-values in Bonferroni multiple comparison test, 544 for claims testing, 375–376 in claims testing, 388–390 in contingency tables, 523 defining, 71, 363 for goodness-of-fit, 511 in hypothesis testing, 363–364 in independent samples, 431 interpreting, 72 for linear correlation, 71–72, 464, 497 for linear correlation coefficient, 464 in one-way ANOVA, 537 rank correlation, 496 from technology, 464, 467, 526, 537 test statistics and, 540 in two proportions, 417–418 Q Quadratic mean, 96 Qualitative data, 14–15 Quantiles, 114 Quantitative data, 14–15 Quartiles, 112–120 defining, 117 www.ebookslides.com 626 Index Questions loaded, order of, R Randomization, 26 Randomized block design, 30–31 Random sample, 27 Random sampling error, 31 Random variable continuous, 187 defining, 186 discrete, 187 numerical, 187 Range, 98 Range rule of thumb, 191, 205–206 for significant values, 101, 191 for standard deviation, 100–101 Range tests, 543 Rank correlation advantages of, 497 critical values, 496 defining, 494 disadvantages of, 497 efficiency, 497 nonlinear patterns, 498–499 notation, 496 procedure, 495 P-value, 496 requirements, 496 software/calculator results, 499–500 test statistic, 496 Ranks defining, 494 handling ties among, 494 Rare event rule, 141–142 hypothesis testing and, 270 for inferential statistics, 192–193 Ratio level, 18 Ratio test, 18 Redundancy, 153 multiplication rule and, 154 Region, 231 Regression, 67–74 advanced concepts, 485–489 bad models, 483–484 basic concepts of, 480–481 correlation and, 484 defining, 73 equation, 73, 480 fitted line plot, 472 good models, 483–484 predictions from, 483–485 scope, 484 software/calculator results, 489 Regression equation slope in, 481 technology and, 482 y-intercept in, 481 Regression line, 480 equation of, 481 formulas for, 481 graphing, 483 notation, 481 requirements, 481 Rejection region, 363 Relative frequency approximation, 135 Relative frequency distribution, 45 Relative frequency histogram, 51–52 Replacements sampling with, 152, 262 sampling without, 152, 262 Replication, 26 in experiment design, 26 Residual plot, 488 Resistant statistics, 82 Response variable, 480 Retrospective study, 29 Right-tailed test, 363 Rigorously controlled design, 31 one-way ANOVA in, 543 Root mean square (RMS), 96 Rounding errors, 87 linear correlation coefficient, 464 measures of center, 86–87 slope, 481–482 two proportions, 417 y-intercept, 481 Round-off rules for coefficient of variation, 106 confidence interval, 303 notation, 307 population mean, 317 population standard deviation, 335 for probability distribution, 189 requirements, 307 for sample size, 307, 323 for z scores, 113 Rubik’s cube, 174 Rule of complementary events, 150 Ryan-Joiner test, 279–280 S Salaries, 526 Salk Vaccine experiment, 25 Sample See also Bootstrap sample defining, dependent, 443–446 independent, 428–437 measurement of, reporting, self-selected, simple random, 27 small, 230 space, 134 variance of, 102–103, 541 voluntary response, Sample data advanced methods, 29–31 basics of, 25–28 collecting, 25–31 Sample mean behavior of, 257–258 central limit theorem and, 267 defining, 257–258 sampling distributions of, 257–259 Sample proportion behavior of, 256–257 as point estimate, 299 sampling distributions of, 256 Sample size determining, 307, 323–324, 338 population mean and, 323–324 population proportion and, 307–308 round-off rule for, 307, 323 software/calculator results, 310 unequal, 543 Sample standard deviation See standard deviation Sample variance behavior of, 260 defining, 259 sampling distributions of, 259–260, 263 Sampling See also Bootstrap resampling cluster, 28 convenience, 28 errors, 31 multistage, 28–29 with replacement, 152, 262 without replacement, 152, 262 stratified, 28 systematic, 28 Sampling distribution, 267 determining, 362 general behavior of, 255 in hypothesis testing, 362 mean and, 255 notation for, 267 proportions and, 255 of sample mean, 257–259 of sample proportion, 256 of sample variance, 259–260, 263 of statistics, 256 variance and, 255 Sampling method, 3, common, 27 Scatterplots, 67–74 defining, 68 interpreting, 462 of z scores, 472 Scheffé test, 544 Self-selected samples, Semi-interquartile range, 118 Sequential events, 165 Shakespeare’s vocabulary, 302 Shuffles, 170 Significance, 251 hypothesis testing for, 359 normal distribution and, 247–248 practical, statistical, Significance level defining, 361 hypothesis testing and, 361–362 Significantly high, 247 Significantly low, 247 Significant results identifying, 192 probability and, 270 Significant values, 101, 114, 191 Sign test, for claims testing, 393 Simple continuity correction, 381 Simple events, 134 Simple random sample, 27, 430 Simulations, 137 Six degrees of separation, 18 Skeletal boxplots, 121 Skewness in boxplots, 119 of histograms, 277 to left, 53 normal distribution and, 277 to right, 53 Slope formulas for, 481 in regression equation, 481 rounding, 481–482 Small samples, 230 Smoking, 543 cancer and, 498 SNK test, 544 Snowden, Eric, 19 Software/calculator results binomial probability distribution, 208 confidence interval, 338 contingency tables, 531 for correlation, 472–473 for dependent samples, 447–448 goodness-of-fit, 518 graphing, 64 www.ebookslides.com Index hypothesis testing, 381, 395, 404, 422 for independent samples, 435–436 inferences, 422 for matched pairs, 447–448 for means, 326, 395 measures of center, 90–91 measures of variation, 107 normal distribution, 249 normal quantile plots, 280 one-way ANOVA, 546 outliers, 123 Poisson probability distribution, 217 for proportions, 310, 381, 422 rank correlation, 499–500 regression, 489 sample size, 310 standard deviation, 338, 404 for two means, 435–436 z scores, 239 Sort data, 38 Spearman’s rank correlation coefficient, 494, 495, 565 Speed dating, 573 Standard deviation bootstrap sample and, 346 Chebyshev’s theorem, 105 claims testing about, 399–404 for critical thinking, 205–208 defining, 103 for independent samples, 435 population, 332–339 of population, 102 for probability distribution, 189 range rule of thumb for, 100–101 software/calculator results, 338, 404 for two means, 435 Standard error of the mean, 267 Standardized score See z scores Standard normal distribution, 230–231 StatCrunch See Software/calculator results Statdisk See Software/calculator results Statistical methods, Statistical significance, Statistics See also specific types in data science, 20–21 defining, 4, 13 inferential, 141–142 misleading, 16 origins of, probability in, 133–134 resistant, 82 sampling distributions of, 256 Stemplots, 58 Stigler, Stephen, 540 Stocks, 99 Stratified sampling, 28 Student t distribution, 318–319, 570 Subjective probabilities, 136 Surveys, 31 Survivorship bias, Systematic sampling, 28 T Tank serial numbers, 321 t distribution, 318–319 student, 318–319 Teacher evaluations, 468 Technology See also Software/ calculator results for claims testing, 388–389 confidence interval and, 304–305 dependent samples and, 446 P-values and, 467–468, 526 regression equation and, 482 two proportions and, 419 Test of homogeneity, 527–528 Test of significance See Hypothesis testing Test sensitivity, 132 Test specificity, 132 Test statistic See also Hypothesis testing calculation of, 541 claims testing, 387, 394, 399 in contingency tables, 523 effect of mean on, 541 for goodness-of-fit, 511, 517 in hypothesis testing, 362, 470 for matched pairs, 443 notation, 362 for one-way ANOVA, 540 in one-way ANOVA, 540–541 P-value and, 540 rank correlation, 496 for tests of independence, 523 for two dependent samples, 443 TI-83/84 Plus Calculator See Software/calculator results Time-series graph, 58 Tornadoes, 575 Tree diagram, 155 True positive/negative, 132 True zero, 18 t test See Student t distribution Tukey test, 544, 550 Twins, 445 Two-tailed test, 363 Two-way frequency table See Contingency tables Type I errors, 367 Type II errors, 367 U Unbiased estimators, 103, 106–107, 263 defining, 261 in point estimates, 299–300 Unequal sample size, 543 Uniform, 277 Uniform distribution, 229–230, 277 Uniform distribution histograms, 53 Upper class limits, 42 V Value of a statistical life (VSL), 30 Variables advanced concepts, 103–107 continuous random, 187 dependent, 480 discrete random, 187 explanatory, 480 independent, 480 lurking, 26, 469 numerical random, 187 in population mean, 317–326 predictor, 480 random, 186–187 response, 480 software/calculator results, 107 Variance See also Analysis of variance claims testing about, 399–404 population, 332–339 for probability distribution, 189 of samples, 102–103, 541 sampling distributions and, 255 627 Variation basic concepts of, 97–103 coefficient of, 106 comparing, 105–106 in linear correlation, 468–469 measures of, 97–107 of population, 102–103 properties of, 103 Voluntary response sample, VSL See Value of a statistical life W Wald confidence interval, 309 Websites, 579 Weighted means, 89–90 Wilcoxon signed-ranks test, for claims testing, 393 Wildlife, 318 Wilson score confidence interval, 309–310 Witnesses, 421 Word counts, 575 X x, 83 x, sampling distribution, 257 Y Yates’s correction for continuity, 536 Y-intercept formulas for, 481 in regression equation, 481 rounding, 481 Z 0+, 188 Zeros, true, 18 z scores, 112–120 area and, 231, 232, 235 defining, 113 known area and, 236–239 negative, 560 positive, 561 probability with, 231–232 properties of, 113 round-off rule for, 113 scatterplots of, 472 significant values and, 114 software/calculator results, 239 www.ebookslides.com TABLE A-3 t Distribution: Critical t Values Left tail 0.005 a Critical t value (negative) Right tail a Critical t value (positive) Two tails a͞2 Critical t value (negative) a͞2 Critical t value (positive) 0.01 Area in One Tail 0.025 0.10 0.20 6.314 3.078 Degrees of Freedom 0.01 0.02 Area in Two Tails 0.05 63.657 31.821 12.706 0.05 0.10 9.925 6.965 4.303 2.920 1.886 5.841 4.541 3.182 2.353 1.638 4.604 3.747 2.776 2.132 1.533 4.032 3.365 2.571 2.015 1.476 3.707 3.143 2.447 1.943 1.440 3.499 2.998 2.365 1.895 1.415 3.355 2.896 2.306 1.860 1.397 3.250 2.821 2.262 1.833 1.383 10 3.169 2.764 2.228 1.812 1.372 11 3.106 2.718 2.201 1.796 1.363 12 3.055 2.681 2.179 1.782 1.356 13 3.012 2.650 2.160 1.771 1.350 14 2.977 2.624 2.145 1.761 1.345 15 2.947 2.602 2.131 1.753 1.341 16 2.921 2.583 2.120 1.746 1.337 17 2.898 2.567 2.110 1.740 1.333 18 2.878 2.552 2.101 1.734 1.330 19 2.861 2.539 2.093 1.729 1.328 20 2.845 2.528 2.086 1.725 1.325 21 2.831 2.518 2.080 1.721 1.323 22 2.819 2.508 2.074 1.717 1.321 23 2.807 2.500 2.069 1.714 1.319 24 2.797 2.492 2.064 1.711 1.318 25 2.787 2.485 2.060 1.708 1.316 26 2.779 2.479 2.056 1.706 1.315 27 2.771 2.473 2.052 1.703 1.314 28 2.763 2.467 2.048 1.701 1.313 29 2.756 2.462 2.045 1.699 1.311 30 2.750 2.457 2.042 1.697 1.310 31 2.744 2.453 2.040 1.696 1.309 32 2.738 2.449 2.037 1.694 1.309 33 2.733 2.445 2.035 1.692 1.308 34 2.728 2.441 2.032 1.691 1.307 35 2.724 2.438 2.030 1.690 1.306 36 2.719 2.434 2.028 1.688 1.306 37 2.715 2.431 2.026 1.687 1.305 38 2.712 2.429 2.024 1.686 1.304 39 2.708 2.426 2.023 1.685 1.304 40 2.704 2.423 2.021 1.684 1.303 45 2.690 2.412 2.014 1.679 1.301 50 2.678 2.403 2.009 1.676 1.299 60 2.660 2.390 2.000 1.671 1.296 70 2.648 2.381 1.994 1.667 1.294 80 2.639 2.374 1.990 1.664 1.292 90 2.632 2.368 1.987 1.662 1.291 100 2.626 2.364 1.984 1.660 1.290 200 2.601 2.345 1.972 1.653 1.286 300 2.592 2.339 1.968 1.650 1.284 400 2.588 2.336 1.966 1.649 1.284 500 2.586 2.334 1.965 1.648 1.283 1000 2.581 2.330 1.962 1.646 1.282 2000 2.578 2.328 1.961 1.646 1.282 Large 2.576 2.326 1.960 1.645 1.282 www.ebookslides.com NEGATIVE z Scores z TABLE A-2 Standard Normal (z) Distribution: Cumulative Area from the LEFT z 00 - 3.50 and lower 01 02 03 04 05 06 07 08 09 0001 - 3.4 - 3.3 0003 0003 0003 0003 0003 0003 0003 0003 0003 0002 0005 0005 0005 0004 0004 0004 0004 0004 0004 0003 - 3.2 0007 0007 0006 0006 0006 0006 0006 0005 0005 0005 - 3.1 0010 0009 0009 0009 0008 0008 0008 0008 0007 0007 - 3.0 0013 0013 0013 0012 0012 0011 0011 0011 0010 0010 - 2.9 0019 0018 0018 0017 0016 0016 0015 0015 0014 0014 - 2.8 0026 0025 0024 0023 0023 0022 0021 0021 0020 0019 - 2.7 0035 0034 0033 0032 0031 0030 0029 0028 0027 0026 - 2.6 0047 0045 0044 0043 0041 0040 0039 0038 0037 0036 - 2.5 0062 0060 0059 0057 0055 0054 0052 0051 0049 0048 - 2.4 0082 0080 0078 0075 0073 0071 0069 0068 0066 0064 - 2.3 0107 0104 0102 0099 0096 0094 0091 0089 0087 0084 - 2.2 0139 0136 0132 0129 0125 0122 0119 0116 0113 0110 - 2.1 0179 0174 0170 0166 0162 0158 0154 0150 0146 0143 - 2.0 0228 0222 0217 0212 0207 0202 0197 0192 0188 0183 - 1.9 0287 0281 0274 0268 0262 0256 0250 0244 0239 0233 - 1.8 0359 0351 0344 0336 0329 0322 0314 0307 0301 0294 - 1.7 0446 0436 0427 0418 0409 0401 0392 0384 0375 0367 - 1.6 0548 0537 0526 0516 0505 0495 0485 0475 0465 0455 - 1.5 0668 0655 0643 0630 0618 0606 0594 0582 0571 0559 - 1.4 0808 0793 0778 0764 0749 0735 0721 0708 0694 0681 - 1.3 0968 0951 0934 0918 0901 0885 0869 0853 0838 0823 - 1.2 1151 1131 1112 1093 1075 1056 1038 1020 1003 0985 - 1.1 1357 1335 1314 1292 1271 1251 1230 1210 1190 1170 - 1.0 1587 1562 1539 1515 1492 1469 1446 1423 1401 1379 - 0.9 1841 1814 1788 1762 1736 1711 1685 1660 1635 1611 - 0.8 2119 2090 2061 2033 2005 1977 1949 1922 1894 1867 - 0.7 2420 2389 2358 2327 2296 2266 2236 2206 2177 2148 - 0.6 2743 2709 2676 2643 2611 2578 2546 2514 2483 2451 - 0.5 3085 3050 3015 2981 2946 2912 2877 2843 2810 2776 - 0.4 3446 3409 3372 3336 3300 3264 3228 3192 3156 3121 - 0.3 3821 3783 3745 3707 3669 3632 3594 3557 3520 3483 - 0.2 4207 4168 4129 4090 4052 4013 3974 3936 3897 3859 - 0.1 4602 4562 4522 4483 4443 4404 4364 4325 4286 4247 - 0.0 5000 4960 4920 4880 4840 4801 4761 4721 4681 4641 NOTE: For values of z below - 3.49, use 0.0001 for the area *Use these common values that result from interpolation: z Score Area - 1.645 0.0500 - 2.575 0.0050 * * (continued ) www.ebookslides.com NEGATIVE z Scores z TABLE A-2 Standard Normal (z) Distribution: Cumulative Area from the LEFT z 00 01 02 03 04 05 06 07 08 09 0003 0003 0003 0003 0003 0003 0003 0003 0003 0002 - 3.3 0005 0005 0005 0004 0004 0004 0004 0004 0004 0003 - 3.2 0007 0007 0006 0006 0006 0006 0006 0005 0005 0005 - 3.1 0010 0009 0009 0009 0008 0008 0008 0008 0007 0007 - 3.0 0013 0013 0013 0012 0012 0011 0011 0011 0010 0010 - 2.9 0019 0018 0018 0017 0016 0016 0015 0015 0014 0014 - 2.8 0026 0025 0024 0023 0023 0022 0021 0021 0020 0019 - 2.7 0035 0034 0033 0032 0031 0030 0029 0028 0027 0026 - 2.6 0047 0045 0044 0043 0041 0040 0039 0038 0037 0036 - 2.5 0062 0060 0059 0057 0055 0054 0052 0051 0049 0048 - 2.4 0082 0080 0078 0075 0073 0071 0069 0068 0066 0064 - 2.3 0107 0104 0102 0099 0096 0094 0091 0089 0087 0084 - 2.2 0139 0136 0132 0129 0125 0122 0119 0116 0113 0110 - 2.1 0179 0174 0170 0166 0162 0158 0154 0150 0146 0143 - 2.0 0228 0222 0217 0212 0207 0202 0197 0192 0188 0183 - 1.9 0287 0281 0274 0268 0262 0256 0250 0244 0239 0233 - 1.8 0359 0351 0344 0336 0329 0322 0314 0307 0301 0294 - 1.7 0446 0436 0427 0418 0409 0401 0392 0384 0375 0367 - 1.6 0548 0537 0526 0516 0505 0495 0485 0475 0465 0455 - 1.5 0668 0655 0643 0630 0618 0606 0594 0582 0571 0559 - 1.4 0808 0793 0778 0764 0749 0735 0721 0708 0694 0681 - 1.3 0968 0951 0934 0918 0901 0885 0869 0853 0838 0823 - 1.2 1151 1131 1112 1093 1075 1056 1038 1020 1003 0985 - 1.1 1357 1335 1314 1292 1271 1251 1230 1210 1190 1170 - 1.0 1587 1562 1539 1515 1492 1469 1446 1423 1401 1379 - 0.9 1841 1814 1788 1762 1736 1711 1685 1660 1635 1611 - 0.8 2119 2090 2061 2033 2005 1977 1949 1922 1894 1867 - 0.7 2420 2389 2358 2327 2296 2266 2236 2206 2177 2148 - 0.6 2743 2709 2676 2643 2611 2578 2546 2514 2483 2451 - 0.5 3085 3050 3015 2981 2946 2912 2877 2843 2810 2776 - 0.4 3446 3409 3372 3336 3300 3264 3228 3192 3156 3121 - 0.3 3821 3783 3745 3707 3669 3632 3594 3557 3520 3483 - 0.2 4207 4168 4129 4090 4052 4013 3974 3936 3897 3859 - 0.1 4602 4562 4522 4483 4443 4404 4364 4325 4286 4247 - 0.0 5000 4960 4920 4880 4840 4801 4761 4721 4681 4641 - 3.50 and lower 0001 - 3.4 NOTE: For values of z below - 3.49, use 0.0001 for the area *Use these common values that result from interpolation: z Score Area - 1.645 0.0500 - 2.575 0.0050 * * (continued) www.ebookslides.com POSITIVE z Scores z TABLE A-2 (continued) Cumulative Area from the LEFT z 00 01 02 03 04 05 06 07 08 09 0.0 5000 5040 5080 5120 5160 5199 5239 5279 5319 5359 0.1 5398 5438 5478 5517 5557 5596 5636 5675 5714 5753 0.2 5793 5832 5871 5910 5948 5987 6026 6064 6103 6141 0.3 6179 6217 6255 6293 6331 6368 6406 6443 6480 6517 0.4 6554 6591 6628 6664 6700 6736 6772 6808 6844 6879 0.5 6915 6950 6985 7019 7054 7088 7123 7157 7190 7224 0.6 7257 7291 7324 7357 7389 7422 7454 7486 7517 7549 0.7 7580 7611 7642 7673 7704 7734 7764 7794 7823 7852 0.8 7881 7910 7939 7967 7995 8023 8051 8078 8106 8133 0.9 8159 8186 8212 8238 8264 8289 8315 8340 8365 8389 1.0 8413 8438 8461 8485 8508 8531 8554 8577 8599 8621 1.1 8643 8665 8686 8708 8729 8749 8770 8790 8810 8830 1.2 8849 8869 8888 8907 8925 8944 8962 8980 8997 9015 1.3 9032 9049 9066 9082 9099 9115 9131 9147 9162 9177 1.4 9192 9207 9222 9236 9251 9265 9279 9292 9306 9319 1.5 9332 9345 9357 9370 9382 9394 9406 9418 9429 9441 1.6 9452 9463 9474 9484 9495 9505 9515 9525 9535 9545 1.7 9554 9564 9573 9582 9591 9599 9608 9616 9625 9633 1.8 9641 9649 9656 9664 9671 9678 9686 9693 9699 9706 1.9 9713 9719 9726 9732 9738 9744 9750 9756 9761 9767 2.0 9772 9778 9783 9788 9793 9798 9803 9808 9812 9817 2.1 9821 9826 9830 9834 9838 9842 9846 9850 9854 9857 2.2 9861 9864 9868 9871 9875 9878 9881 9884 9887 9890 2.3 9893 9896 9898 9901 9904 9906 9909 9911 9913 9916 2.4 9918 9920 9922 9925 9927 9929 9931 9932 9934 9936 2.5 9938 9940 9941 9943 9945 9946 9948 9949 9951 9952 2.6 9953 9955 9956 9957 9959 9960 9961 9962 9963 9964 2.7 9965 9966 9967 9968 9969 9970 9971 9972 9973 9974 2.8 9974 9975 9976 9977 9977 9978 9979 9979 9980 9981 2.9 9981 9982 9982 9983 9984 9984 9985 9985 9986 9986 3.0 9987 9987 9987 9988 9988 9989 9989 9989 9990 9990 3.1 9990 9991 9991 9991 9992 9992 9992 9992 9993 9993 3.2 9993 9993 9994 9994 9994 9994 9994 9995 9995 9995 3.3 9995 9995 9995 9996 9996 9996 9996 9996 9996 9997 3.4 9997 9997 9997 9997 9997 9997 9997 9997 9997 9998 3.50 and up 9999 NOTE: For values of z above 3.49, use 0.9999 for the area *Use these common values that result from interpolation: z score Area 1.645 0.9500 2.575 0.9950 * * Common Critical Values Confidence Level Critical Value 0.90 1.645 0.95 1.96 0.99 2.575 www.ebookslides.com TABLE A-3 t Distribution: Critical t Values 0.005 0.01 Area in One Tail 0.025 0.05 0.10 0.01 0.02 Area in Two Tails 0.05 0.10 0.20 63.657 31.821 12.706 6.314 3.078 9.925 6.965 4.303 2.920 1.886 5.841 4.541 3.182 2.353 1.638 4.604 3.747 2.776 2.132 1.533 4.032 3.365 2.571 2.015 1.476 3.707 3.143 2.447 1.943 1.440 3.499 2.998 2.365 1.895 1.415 3.355 2.896 2.306 1.860 1.397 3.250 2.821 2.262 1.833 1.383 10 3.169 2.764 2.228 1.812 1.372 11 3.106 2.718 2.201 1.796 1.363 12 3.055 2.681 2.179 1.782 1.356 13 3.012 2.650 2.160 1.771 1.350 14 2.977 2.624 2.145 1.761 1.345 15 2.947 2.602 2.131 1.753 1.341 16 2.921 2.583 2.120 1.746 1.337 17 2.898 2.567 2.110 1.740 1.333 18 2.878 2.552 2.101 1.734 1.330 19 2.861 2.539 2.093 1.729 1.328 20 2.845 2.528 2.086 1.725 1.325 21 2.831 2.518 2.080 1.721 1.323 22 2.819 2.508 2.074 1.717 1.321 23 2.807 2.500 2.069 1.714 1.319 24 2.797 2.492 2.064 1.711 1.318 25 2.787 2.485 2.060 1.708 1.316 26 2.779 2.479 2.056 1.706 1.315 27 2.771 2.473 2.052 1.703 1.314 28 2.763 2.467 2.048 1.701 1.313 29 2.756 2.462 2.045 1.699 1.311 30 2.750 2.457 2.042 1.697 1.310 31 2.744 2.453 2.040 1.696 1.309 32 2.738 2.449 2.037 1.694 1.309 33 2.733 2.445 2.035 1.692 1.308 34 2.728 2.441 2.032 1.691 1.307 35 2.724 2.438 2.030 1.690 1.306 36 2.719 2.434 2.028 1.688 1.306 37 2.715 2.431 2.026 1.687 1.305 38 2.712 2.429 2.024 1.686 1.304 39 2.708 2.426 2.023 1.685 1.304 40 2.704 2.423 2.021 1.684 1.303 45 2.690 2.412 2.014 1.679 1.301 50 2.678 2.403 2.009 1.676 1.299 60 2.660 2.390 2.000 1.671 1.296 70 2.648 2.381 1.994 1.667 1.294 80 2.639 2.374 1.990 1.664 1.292 90 2.632 2.368 1.987 1.662 1.291 100 2.626 2.364 1.984 1.660 1.290 200 2.601 2.345 1.972 1.653 1.286 300 2.592 2.339 1.968 1.650 1.284 400 2.588 2.336 1.966 1.649 1.284 500 2.586 2.334 1.965 1.648 1.283 1000 2.581 2.330 1.962 1.646 1.282 2000 2.578 2.328 1.961 1.646 1.282 Large 2.576 2.326 1.960 1.645 1.282 Degrees of Freedom ... amounts of data such as the following: ■ Terabytes (1012 or 1,000,000,000,000 bytes) of data ■ Petabytes (1015 bytes) of data ■ Exabytes (1018 bytes) of data ■ Zettabytes (1021 bytes) of data... Success MyLab Statistics Online Course for Essentials of Statistics, 6e by Mario F Triola (access code required) MyLab™ Statistics is available to accompany Pearson’s market-leading text offerings...www.ebookslides.com 6th EDITION ESSENTIALS OF STATISTICS www.ebookslides.com www.ebookslides.com 6th EDITION ESSENTIALS OF STATISTICS MARIO F TRIOLA Special Contributions by Laura lossi, Broward College