Area 0 z TABLE 3 Areas under the Normal Curve, pages 688–689 z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 (cid:1)3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 (cid:1)3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 (cid:1)3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005 (cid:1)3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 (cid:1)3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 (cid:1)2.9 .0019 .0018 .0017 .0017 .0016 .0016 .0015 .0015 .0014 .0014 (cid:1)2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 (cid:1)2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 (cid:1)2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 (cid:1)2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 (cid:1)2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 (cid:1)2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 (cid:1)2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 (cid:1)2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 (cid:1)2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 (cid:1)1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 (cid:1)1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 (cid:1)1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 (cid:1)1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 (cid:1)1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 (cid:1)1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0722 .0708 .0694 .0681 (cid:1)1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 (cid:1)1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 (cid:1)1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 (cid:1)1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 (cid:1)0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 (cid:1)0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 (cid:1)0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 (cid:1)0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 (cid:1)0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 (cid:1)0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 (cid:1)0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 (cid:1)0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 (cid:1)0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 (cid:1)0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 TABLE 3 (continued) 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 List of Applications Business and Economics Paper strength, 274 Creation, 136 Actuaries, 172 Particle board, 574 Defective computer chips, 207 Advertising campaigns, 655 Product quality, 431 Defective equipment, 171 Airline occupancy rates, 361 Property values, 642, 649 Dieting, 322 America’s market basket, 415–416 Raisins, 408–409 Different realities, 327 Assembling electronic equipment, 460 Rating tobacco leaves, 666 Dinner at Gerards, 143 Auto accidents, 328 Real estate prices, 113 Driving emergencies, 72 Auto insurance, 58, 415, 477 School workers, 339–340, 383–384 Elevator capacities, 235 Baseball bats, 286 Service times, 32 Eyeglasses, 135 Bidding on construction jobs, 476–477 Shipping charges, 172 Fast food and gas stations, 197 Black jack, 286 Sports salaries, 59 Fear of terrorism, 46 Brass rivets, 286 Starbucks, 59 Football strategies, 162 Charitable contributions, 102 Strawberries, 514, 521, 533 Free time, 101 Coal burning power plant, 286 Supermarket prices, 659–660 Freestyle swimmers, 409 Coffee breaks, 172 Tax assessors, 416–417 Going to the moon, 259–260 College textbooks, 563–564 Tax audits, 236 Golfing, 158 Color TVs, 638 Teaching credentials, 207–208 Gourmet cooking, 642, 649 Construction projects, 574–575 Telecommuting, 609–610 GPAs, 335 Consumer confidence, 306 Telemarketers, 195 GRE scores, 466 Consumer Price Index, 101–102 Timber tracts, 73 Hard hats, 424 Cordless phones, 124–125 Tuna fish, 59, 73, 90, 397, 407–408, 431, Harry Potter, 196 Corporate profits, 565 461–462 Hockey, 538 Cost of flying, 520–521 Utility bills in southern California, 66, 86 Home security systems, 196 Cost of lumber, 462, 466 Vacation destinations, 217 Hotel costs, 367–368 Deli sales, 274 Vehicle colors, 624 Human heights, 235 Does college pay off?, 362 Warehouse shopping, 477–478 Hunting season, 335 Drilling oil wells, 171 Water resistance in textiles, 475 In-home movies, 244 Economic forecasts, 236 Worker error, 162 Instrument precision, 423–424 e-shopping, 317 Insuring your diamonds, 171–172 Flextime, 362 General Interest Itineraries, 142–143 Fortune 500 revenues, 58 “900” numbers, 307 Jason and Shaq, 157–158 Gas mileage, 475 100-meter run, 136, 143 JFK assassination, 609 Glare in rearview mirrors, 475 9/11 conspiracy, 383 Length, 513 Grant funding, 156 9-1-1, 322 Letterman or Leno, 170–171 Grocery costs, 113 Accident prone, 204 M&M’S, 101, 326–327, 377 Hamburger meat, 85, 234–235, Airport safety, 204 Machine breakdowns, 649 316–317, 361, 399 Airport security, 162 Major world lakes, 43–44 HDTVs, 59, 114, 526 Armspan and height, 513–514, 522 Man’s best friend, 197, 373 Homeschool teachers, 623–624 Art critics, 665–666 Men on Mars, 307 Housing prices, 532–533 Barry Bonds, 93 Noise and stress, 368 Inspection lines, 157 Baseball and steroids, 327 Old Faithful, 73 Internet on-the-go, 46–47 Baseball fans, 327 PGA, 171 Interstate commerce, 176 Baseball stats, 539 Phospate mine, 235 Job security, 212 Batting champions, 32–33 Playing poker, 143 Legal immigration, 306, 334 Birth order and college success, 327 Presidential vetoes, 85 Lexus, Inc., 113–114 Birthday problem, 156 President’s kids, 73–74 Light bulbs, 424 Braking distances, 235 Professor Asimov, 512, 521, 525 Line length, 31–32 Brett Favre, 74, 122, 398 Rating political candidates, 665 Loading grain, 236 Car colors, 196 Red dye, 416 Lumber specs, 286 Cell phone etiquette, 251–252 Roulette, 135, 171 Movie marketing, 376–377 Cheating on taxes, 162 Sandwich generation, 613 MP3 players, 316 Christmas trees, 235 Smoke detectors, 157 Multimedia kids, 306 Colored contacts, 372 Soccer injuries, 157 Nuclear power plant, 286 Comparing NFL quarterbacks, 85, 409 Starbucks or Peet’s, 156–157 Operating expenses, 334 Competitive running, 665 Summer vacations, 306–307 Packaging hamburger meat, 72 Cramming, 144 SUVs, 317 (continued) List of Applications (continued) Tennis, 171, 236 Good tasting medicine, 660 Weights of turtles, 638 Tennis racquets, 665 Ground or air, 416 What’s normal?, 49, 86, 317, 323, 362, 368 Time on task, 59 Hazardous waste, 33 Whitefly infestation, 196 Tom Brady, 533 Healthy eating, 367 Tomatoes, 274 Healthy teeth, 407, 416 Social Sciences Top 20 movies, 33 Heart rate and exercise, 655 Traffic control, 649 Hormone therapy and Alzheimer’s A female president?, 338–339 Traffic problems, 143 disease, 377 Achievement scores, 573–574 Vacation plans, 143 HRT, 377 Achievement tests, 512–513, 545 Walking shoes, 549 Hungry rats, 307 Adolescents and social stress, 381 What to wear, 142 Impurities, 431–432 American presidents, 32 WNBA, 143 Invasive species, 361–362 Anxious infants, 608–609 Jigsaw puzzles, 649–650 Back to work, 17 Lead levels in blood, 642–643 Catching a cold, 327 Life Sciences Lead levels in drinking water, 367 Choosing a mate, 157 Achilles tendon injuries, 274–275, 362 Legal abortions, 291, 317 Churchgoing and age, 614 Acid rain, 316 Less red meat, 335, 572–573 Disabled students, 113 Air pollution, 520, 525, 565 Lobsters, 398, 538 Discovery-based teaching, 621 Alzheimer’s disease, 637 Long-term care, 613–614 Drug offenders, 156 Archeological find, 47, 65, 74, 409 Losing weight, 280 Drug testing, 156 Baby’s sleeping position, 377 Mandatory health care, 608 Election 2008, 16 Back pain, 196–197 Measurement error, 273–274 Eye movement, 638 Bacteria in drinking water, 236 Medical diagnostics, 162 Faculty salaries, 273 Bacteria in water, 274 Mercury concentration in dolphins, 84–85 Gender bias, 144, 171, 207 Bacteria in water samples, 204–205 MMT in gasoline, 368 Generation Next, 327–328, 380 Biomass, 306 Monkey business, 144 Hospital survey, 143 Birth order and personality, 58 Normal temperatures, 274 Household size, 102, 614 Blood thinner, 259 Ore samples, 72 Images and word recall, 650 Blood types, 196 pH in rainfall, 335 Intensive care, 204 Body temperature and heart rate, 539 pH levels in water, 655 Jury duty, 135–136 Breathing rates, 72, 235 Physical fitness, 499 Laptops and learning, 522, 526 Bulimia, 398 Plant genetics, 157, 372 Medical bills, 196 Calcium, 461, 465–466 Polluted rain, 335 Memory experiments, 417 Calcium content, 32 Potassium levels, 274 Midterm scores, 125 Cancer in rats, 259 Potency of an antibiotic, 362 Music in the workplace, 417 Cerebral blood flow, 235 Prescription costs, 280 Native American youth, 259 Cheese, 539 Pulse rates, 236 No pass, no play rule for athletics, 162 Chemical experiment, 512 Purifying organic compounds, 398 Organized religion, 31 Chemotherapy, 638 Rain and snow, 124 Political corruption, 334–335 Chicago weather, 195 Recovery rates, 643 Preschool, 31 Childhood obesity, 371–372 Recurring illness, 31 Race distributions in the Armed Cholesterol, 399 Red blood cell count, 32, 399 Forces, 16–17 Clopidogrel and aspirin, 377 Runners and cyclists, 408, 415, 431 Racial bias, 259 Color preferences in mice, 196 San Andreas Fault, 306 Reducing hostility, 460 Cotton versus cucumber, 573 Screening tests, 162–163 Rocking the vote, 317 Cure for insomnia, 372–373 Seed treatments, 208 SAT scores, 195–196, 431, 445 Cure for the common cold, 366–367 Selenium, 322, 335 Smoking and cancer, 157 Deep-sea research, 614 Slash pine seedlings, 475–476 Social Security numbers, 72–73 Digitalis and calcium uptake, 476 Sleep deprivation, 512 Social skills training, 538, 666 Diseased chickens, 613 Smoking and lung capacity, 398 Spending patterns, 609 Disinfectants, 408 Sunflowers, 235 Starting salaries, 322–323, 367 DissolvedO content,397–398,409,461,638 Survival times, 50, 73, 85–86 Student ratings, 665 2 Drug potency, 424 Swampy sites, 460–461, 465, 655 Teaching biology, 322 E. colioutbreak, 205 Sweet potato whitefly, 372 Teen magazines, 212 Early detection of breast cancer, 372 Taste test for PTC, 197 Test interviews, 513 Excedrin or Tylenol, 328 Titanium, 408 Union, yes!, 327 FDA testing, 172 Toxic chemicals, 660 Violent crime, 161–162 Fruit flies, 136 Treatment versus control, 376 Want to be president?, 16 Geothermal power, 538–539 Vegi-burgers, 564–565 Who votes?, 373 Glucose tolerance, 466 Waiting for a prescription, 609 YouTube, 566 How Do I Construct a Stem and Leaf Plot? 20 How Do I Calculate Probabilities for the Sample Mean x(cid:1)? How Do I Construct a Relative Frequency Histogram? 27 268 How Do I Calculate Sample Quartiles? 79 How Do I Calculate Probabilities for the Sample Proportionpˆ? 277 How Do I Calculate the Correlation Coefficient? 111 How Do I Calculate the Regression Line? 111 How Do I Estimate a Population Mean or Proportion? 303 What’s the Difference between Mutually Exclusive and How Do I Choose the Sample Size? 331 Independent Events? 153 Rejection Regions, p-Values, and Conclusions 355 How Do I Use Table 1 to Calculate Binomial Probabilities? How Do I Calculate b? 360 190 HowDoICalculatePoissonProbabilitiesUsingtheFormula? How Do I Decide Which Test to Use? 432 198 How Do I Know Whether My Calculations Are Accurate? How Do I Use Table 2 to Calculate Poisson Probabilities? 459 199 How Do I Make Sure That My Calculations Are Correct? How Do I Use Table 3 to Calculate Probabilities under the 508 Standard Normal Curve? 228 How Do I Determine the Appropriate Number of Degrees How Do I Calculate Binomial Probabilities Using the of Freedom? 606, 611 Normal Approximation? 240 Index of Applet Figures CHAPTER 1 CHAPTER 8 Figure 1.17 Building a Dotplot applet Figure 8.10 Interpreting Confidence Intervals applet Figure 1.18 Building a Histogram applet Figure 1.19 Flipping Fair Coins applet CHAPTER 9 Figure 1.20 Flipping Fair Coins applet Figure 9.7 Large Sample Test of a Population Mean applet CHAPTER 2 Figure 9.9 Power of a z-Test applet Figure 2.4 How Extreme Values Affect the Mean and Median applet CHAPTER 10 Figure 2.9 Why Divide n(cid:1)1? Figure 10.3 Student’s tProbabilities applet Figure 2.19 Building a Box Plot applet Figure 10.5 Comparing tandzapplet Figure 10.9 Small Sample Test of a Population Mean CHAPTER 3 applet Figure 3.6 Building a Scatterplot applet Figure 10.12 Two-Sample tTest: Independent Samples Figure 3.9 Exploring Correlation applet applet Figure 3.12 How a Line Works applet Figure 10.17 Chi-Square Probabilities applet CHAPTER 4 Figure 10.21 FProbabilities applet Figure 4.6 Tossing Dice applet CHAPTER 11 Figure 4.16 Flipping Fair Coins applet Figure 11.6 FProbabilities applet Figure 4.17 Flipping Weighted Coins applet CHAPTER 12 CHAPTER 5 Figure 12.4 Method of Least Squares applet Figure 5.2 Calculating Binomial Probabilities applet Figure 12.7 tTest for the Slope applet Figure 5.3 Java Applet for Example 5.6 Figure 12.17 Exploring Correlation applet CHAPTER 6 CHAPTER 14 Figure 6.7 Visualizing Normal Curves applet Figure 14.1 Goodness-of-Fit applet Figure 6.14 Normal Distribution Probabilities applet Figure 14.2 Chi-Square Test of Independence applet Figure 6.17 Normal Probabilities and z-Scores applet Figure 14.4 Chi-Square Test of Independence applet Figure 6.21 Normal Approximation to Binomial Probabilities applet CHAPTER 7 Figure 7.7 Central Limit Theorem applet Figure 7.10 Normal Probabilities for Means applet a t a TABLE 4 df t t t t t df Critical Values .100 .050 .025 .010 .005 of t 1 3.078 6.314 12.706 31.821 63.657 1 page 691 2 1.886 2.920 4.303 6.965 9.925 2 3 1.638 2.353 3.182 4.541 5.841 3 4 1.533 2.132 2.776 3.747 4.604 4 5 1.476 2.015 2.571 3.365 4.032 5 6 1.440 1.943 2.447 3.143 3.707 6 7 1.415 1.895 2.365 2.998 3.499 7 8 1.397 1.860 2.306 2.896 3.355 8 9 1.383 1.833 2.262 2.821 3.250 9 10 1.372 1.812 2.228 2.764 3.169 10 11 1.363 1.796 2.201 2.718 3.106 11 12 1.356 1.782 2.179 2.681 3.055 12 13 1.350 1.771 2.160 2.650 3.012 13 14 1.345 1.761 2.145 2.624 2.977 14 15 1.341 1.753 2.131 2.602 2.947 15 16 1.337 1.746 2.120 2.583 2.921 16 17 1.333 1.740 2.110 2.567 2.898 17 18 1.330 1.734 2.101 2.552 2.878 18 19 1.328 1.729 2.093 2.539 2.861 19 20 1.325 1.725 2.086 2.528 2.845 20 21 1.323 1.721 2.080 2.518 2.831 21 22 1.321 1.717 2.074 2.508 2.819 22 23 1.319 1.714 2.069 2.500 2.807 23 24 1.318 1.711 2.064 2.492 2.797 24 25 1.316 1.708 2.060 2.485 2.787 25 26 1.315 1.706 2.056 2.479 2.779 26 27 1.314 1.703 2.052 2.473 2.771 27 28 1.313 1.701 2.048 2.467 2.763 28 29 1.311 1.699 2.045 2.462 2.756 29 (cid:2) 1.282 1.645 1.960 2.326 2.576 (cid:2) SOURCE: From “Table of Percentage Points of the t-Distribution,”Biometrika32 (1941):300. Reproduced by permission of the BiometrikaTrustees. Introduction to Probability and Statistics 13th EDITION William Mendenhall University of Florida, Emeritus Robert J. Beaver University of California, Riverside, Emeritus Barbara M. Beaver University of California, Riverside Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Introduction to Probability and © 2009, 2006 Brooks/Cole, Cengage Learning Statistics, Thirteenth Edition ALL RIGHTS RESERVED. No part of this work covered by the William Mendenhall, Robert J. Beaver, copyright herein may be reproduced, transmitted, stored, or used Barbara M. 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Purchase any of our products at your local college store or at our preferred online store www.ichapters.com. Printed in Canada 1 2 3 4 5 6 7 12 11 10 09 08 Preface Every time you pick up a newspaper or a magazine, watch TV, or surf the Internet, you encounter statistics. Every time you fill out a questionnaire, register at an online web- site, or pass your grocery rewards card through an electronic scanner, your personal information becomes part of a database containing your personal statistical informa- tion. You cannot avoid the fact that in this information age, data collection and analy- sis are an integral part of our day-to-day activities. In order to be an educated consumer and citizen, you need to understand how statistics are used and misused in our daily lives. To that end we need to “train your brain” for statistical thinking—a theme we emphasize throughout the thirteenth edition by providing you with a “personal trainer.” THE SECRET TO OUR SUCCESS The first college course in introductory statistics that we ever took used Introduction to Probability and Statisticsby William Mendenhall. Since that time, this text—currently in the thirteenth edition—has helped several generations of students understand what statistics is all about and how it can be used as a tool in their particular area of applica- tion. The secret to the success of Introduction to Probability and Statisticsis its ability to blend the old with the new. With each revision we try to build on the strong points of previous editions, while always looking for new ways to motivate, encourage, and interest students using new technological tools. HALLMARK FEATURES OF THE THIRTEENTH EDITION The thirteenth edition retains the traditional outline for the coverage of descriptive and inferential statistics. This revision maintains the straightforward presentation of the twelfth edition. In this spirit, we have continued to simplify and clarify the language and to make the language and style more readable and “user friendly”—without sacri- ficing the statistical integrity of the presentation. Great effort has been taken to “train your brain” to explain not only how to apply statistical procedures, but also to explain • how to meaningfully describe real sets of data • what the results of statistical tests mean in terms of their practical applications • how to evaluate the validity of the assumptions behind statistical tests • what to do when statistical assumptions have been violated