Introducció a la Probabilitat i Estadística - PDF

 Table 4 Critical Values of t, pages 692–963   df t.100 t.050 t.025...

 Table 4 Critical Values of t, pages 692–963   df t.100 t.050 t.025 t.010 t.005 df a     1 3.078 6.314 12.706 31.821 63.657 1 ta     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   30 1.310 1.697   2.042   2.457   2.750 30   31 1.309 1.696   2.040   2.453   2.744 31   32 1.309 1.694   2.037   2.449   2.738 32   33 1.308 1.692   2.035   2.445   2.733 33   34 1.307 1.691   2.032   2.441   2.728 34   35 1.306 1.690   2.030   2.438   2.724 35   36 1.306 1.688   2.028   2.434   2.719 36   37 1.305 1.687   2.026   2.431   2.715 37   38 1.304 1.686   2.024   2.429   2.712 38   39 1.304 1.685   2.023   2.426   2.708 39   40 1.303 1.684   2.021   2.423   2.704 40   45 1.301 1.679   2.014   2.412   2.690 45   50 1.299 1.676   2.009   2.403   2.678 50   55 1.297 1.673   2.004   2.396   2.668 55   60 1.296 1.671   2.000   2.390   2.660 60   65 1.295 1.669   1.997   2.385   2.654 65   70 1.294 1.667   1.994   2.381   2.648 70   80 1.292 1.664   1.990   2.374   2.639 80   90 1.291 1.662   1.987   2.368   2.632 90 100 1.290 1.660   1.984   2.364   2.626 100 200 1.286 1.653   1.972   2.345   2.601 200 300 1.284 1.650   1.968   2.339   2.592 300 400 1.284 1.649   1.966   2.336   2.588 400 500 1.283 1.648   1.965   2.334   2.586 500 inf. 1.282 1.645 1.96   2.326   2.576 inf. Source: Percentage points calculated using Minitab software. Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Body temperature and heart rate 542 Measurement error 263 Social Sciences Breathing rates 74, 93, 441 Medical diagnostics 162 Achievement scores 581 Bulimia 392 Mercury concentration in dolphins 84, 594 Achievement tests 75, 515, 550 Calcium 440, 460, 464 Metal corrosion and soil acids 572 Adolescents and social stress 376 Calcium content 25 Metabolism and weight gain 552 Alcohol and altitude 442 Cancer survivor rates 12, 187 Monkey business 144 American Presidents-age at death 26 Cerebral blood flow 226, 263, 391, 419 MRIs 164 Animation helps 502 Chemical experiment 306, 515 Nematodes 549 Anxious infants 612 Chemotherapy 642 Omega-3 Fats 250 Back to work 17 Chicago weather 186 Ore samples 74 Books or iPads? 401 Chirping crickets 111, 523, 528 Parasites in foxes 94 Boomers, Xers and Millennial Men 375 Chloroform 92 PCBs 377 Catching a cold 318, 321, 630 Cholesterol 393 Pearl millet 340 Choosing a mate 158 Citrus red mite 325 pH in rainfall 326 Discovery-based teaching 627 Color preferences in mice 210 pH levels in water 660 Drug offenders 156 Cotton versus cucumber 580 Physical fitness 500, 612 Drug testing 156 Cure for insomnia 364 Plant density 208 Eye movement 642 Cure for the common cold 358 Plant genetics 157, 188, 234, 363 Faculty salaries 263, 486, 501 Deep-sea research 617 Plant science 537 Good at math? 460 Diabetes in children 208 Polluted seawater 67, 84 Graduate teaching assistants 628 Digitalis and calcium uptake 475 Pollution 326, 499, 678 Hospital survey 143 Disinfectants 402 Potassium levels 264 Household size 101, 617 Dissolved O2 content 392, 403, 459, 642 Potency of an antibiotic 353 Images and word recall 251, 654 Drugs for hypertension 92 Pulse rates 49, 227 Intensive care 195 Drug potency 420 Purifying organic compounds 392 Jury duty 136 E. coli outbreaks 196 Rain and snow 121 Laptops and learning 51, 524, 528 Early detection of breast cancer 363 Recovery rates 647 Math and art 677 Enzymes 401 Recurring illness 32, 91 Medical bills 189 Excedrin or Tylenol 318 Red blood cell count 25, 393 Memory experiments 412 FDA testing 175 Rh factor 233, 285 Midterm scores 118 Fossils 440 Ring-necked pheasants 440 Music in the workplace 412 Fruit flies 136 Runners and cyclists 402, 428, 443 No pass-no play rule for athletics 162 Geothermal power 542 San Andreas Fault 296 Organized religion 25 Genetic defects 233 Screening tests 162 Political corruption 326 Gestation times 121, 226, 523 Sea urchins 440 Preschool 33 Glucose tolerance 464 Seed treatments 199 Racial bias 250 Good tasting medicine 619, 665 Selenium 311, 326 Reaction times 410, 441, 442, Ground or air 411 Shade or sun? 440 497, 498 Gulf oil spill 48 Slash pine seedlings 474 Reducing hostility 458 Hazardous waste 26, 123 Sleep deprivation 515, 523 Same-sex marriage 284, 306 Healthy eating 358, 579 Smoking 331, 392 SAT scores 92, 187, 313, 359, Healthy teeth 401, 411 Sodium hydroxide 439 376, 427 Heart rate and exercise 465, 659 Spraying fruit trees 358 Smoking and cancer 157 Hormone therapy and Alzheimer’s disease 368 Sunflowers 227, 332 Snacking and TV 242 Human body temperatures 50, 95, 242, 264, 307, Survival times 32, 74, 85 Social ambivalence 92 313, 353, 359 Swampy sites 459, 464, 659 Social Security numbers 74 Hungry rats 297 Sweet potato whitefly 363 Social skills training 110, 541, 671 Impurities 428, 439 Tai Chi and fibromyalgia 251, 368 Spending patterns 612 Iodine concentration 331 Taste test for PTC 189 Starting salaries 312, 321, 359 Jigsaw puzzles 654 Tay-Sachs disease 188 Student ratings 671 Lead levels in blood 647 Titanium 402 Teaching biology 312 Lead levels in drinking water 358 Toxic chemicals 664 Test interviews 119, 515 Less red meat 321, 579 Weights of babies 225, 263, 305, 352 Unbiased choices 144, 174, 199 Lobsters 392, 541 Weights of turtles 642 Union Yes! 318 Long stemmed roses 92 Whitefly infestation 210, 499 Violent crime 162 Lung cancer 233 White tailed deer 376 Want to be President? 16 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Edition Introduction 15 to Probability and Statistics Metric Version William Mendenhall, III 1925–2009 Robert J. Beaver University of California, Riverside, Emeritus Barbara M. Beaver University of California, Riverside, Emerita Australia Brazil Mexico Singapore United Kingdom United States Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). 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Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Brief Contents introduction: WHAT IS STATISTICS?  1 1 Describing Data with Graphs  7 2 Describing Data with Numerical Measures  54 3 Describing Bivariate Data  96 4 Probability  126 5 Discrete Probability Distributions  167 6 The Normal Probability Distribution  212 7 Sampling Distributions  245 8 Large-Sample Estimation  288 9 Large-Sample Tests of Hypotheses  335 10 Inference from Small Samples  380 11 The Analysis of Variance  445 12 Simple Linear Regression and Correlation  503 13 Multiple Linear Regression Analysis  555 14 Analysis of Categorical Data  599 15 Nonparametric Statistics  633 Appendix i  681 data sources  714 answers to selected exercises  727 index  745 iii Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Contents Introduction: What Is Statistics? 1 The Population and the Sample 3 Descriptive and Inferential Statistics 3 Achieving the Objective of Inferential Statistics: The Necessary Steps 4 Keys for Successful Learning 5 1 Describing Data with Graphs 7 1.1 Variables and Data 8 Types of Variables 9 Exercises  11 1.2 Graphs for Categorical Data 12 Exercises  15 1.3 Graphs for Quantitative Data 17 Pie Charts and Bar Charts 17 Line Charts 19 Dotplots 20 Stem and Leaf Plots 20 Interpreting Graphs with a Critical Eye 22 Exercises  24 1.4 Relative Frequency Histograms 27 Exercises  31 Chapter Review 35 Technology Today 35 Reviewing What You’ve Learned 47 Case Study: How Is Your Blood Pressure? 53 2 Describing Data with Numerical Measures 54 Introduction 55 2.1 Measures of Center 55 Exercises  59 2.2 Measures of Variability 61 Exercises  66 iv Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Contents v 2.3 Understanding and Interpreting the Standard Deviation 67 Tchebysheff’s Theorem 67 The Empirical Rule 69 Approximating s Using the Range 71 Exercises  73 2.4 Measures of Relative Standing 76 z-Scores 76 Percentiles and Quartiles 77 The Five-Number Summary and the Box Plot 80 Exercises  83 Chapter Review 86 Technology Today 87 Reviewing What You’ve Learned 91 Case Study: The Boys of Summer 95 3 Describing Bivariate Data 96 Introduction 97 3.1 Describing Bivariate Categorical Data 97 Exercises  99 3.2 Describing Bivariate Quantitative Data 101 Scatterplots 101 The Correlation Coefficient 104 The Least-Squares Line 106 Exercises  109 Chapter Review 112 Technology Today 112 Reviewing What You’ve Learned 118 Case Study: Are Your Clothes Really Clean? 124 4 Probability 126 Introduction 127 4.1 Events and the Sample Space 127 Exercises  130 4.2 Calculating Probabilities Using Simple Events 131 Exercises  134 4.3 Useful Counting Rules 137 Using the TI-83/84 Plus Calculator 142 Exercises  142 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. vi Contents 4.4 Rules for Calculating Probabilities 144 Calculating Probabilities for Unions and Complements 146 Calculating Probabilities for Intersections 148 Exercises  155 4.5 Bayes’ Rule 158 Exercises  161 Chapter Review 163 Reviewing What You’ve Learned 163 Case Study: Probability and Decision Making in the Congo 166 5 Discrete Probability Distributions 167 5.1 Discrete Random Variables and Their ­Probability Distributions 168 Random Variables 168 Probability Distributions 168 The Mean and Standard Deviation for a Discrete Random Variable 170 Exercises  174 5.2 The Binomial Probability Distribution 176 Exercises  185 5.3 The Poisson Probability Distribution 189 Exercises  194 5.4 The Hypergeometric Probability Distribution 196 Exercises  198 Chapter Review 200 Technology Today 201 Reviewing What You’ve Learned 206 Case Study: A Mystery: Cancers Near a Reactor 211 6 The Normal Probability Distribution 212 6.1 Probability Distributions for Continuous Random Variables 213 The Continuous Uniform Probability Distribution 215 The Exponential Probability Distribution 216 Exercises  217 6.2 The Normal Probability Distribution 218 The Standard Normal Random Variable 219 Calculating Probabilities for a General Normal Random Variable 222 Exercises  225 6.3 The Normal Approximation to the Binomial Probability Distribution 228 Exercises  232 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Contents vii Chapter Review 235 Technology Today 235 Reviewing What You’ve Learned 241 Case Study: “Are You Going to Curve the Grades?” 244 7 Sampling Distributions 245 Introduction 246 7.1 Sampling Plans and Experimental Designs 246 Exercises  249 7.2 Statistics and Sampling Distributions 252 Exercises  254 7.3 The Central Limit Theorem and the Sample Mean 255 The Central Limit Theorem 255 The Sampling Distribution of the Sample Mean 258 Standard Error of the Sample Mean 259 Exercises  262 7.4 Assessing Normality 264 7.5 The Sampling Distribution of the Sample Proportion 268 Exercises  271 7.6 A Sampling Application: Statistical Process Control (Optional) 273 A Control Chart for the Process Mean: The x Chart 274 A Control Chart for the Proportion Defective: The p Chart 276 Exercises  278 Chapter Review 280 Technology Today 281 Reviewing What You’ve Learned 284 Case Study: Sampling the Roulette at Monte Carlo 287 8 Large-Sample Estimation 288 8.1 Where We’ve Been and Where We’re Going 289 Statistical Inference 289 Types of Estimators 290 8.2 Point Estimation 291 Exercises  296 8.3 Interval Estimation 298 Constructing a Confidence Interval 298 Large-Sample Confidence Interval for a Population Mean  300 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. viii Contents Interpreting the Confidence Interval 301 Large-Sample Confidence Interval for a Population Proportion p 303 Using Technology 304 Exercises  304 8.4 Estimating the Difference Between Two Population Means 307 Exercises  311 8.5 Estimating the Difference Between Two Binomial Proportions 313 Using Technology 316 Exercises  316 8.6 One-Sided Confidence Bounds 319 Exercises  320 8.7 Choosing the Sample Size 322 Exercises  325 Chapter Review 326 Technology Today 327 Reviewing What You’ve Learned 330 Case Study: How Reliable Is That Poll? CBS News: How and Where America Eats 333 9 Large-Sample Tests of Hypotheses 335 Introduction 336 9.1 A Statistical Test of Hypothesis 336 Exercises  339 9.2 A Large-Sample Test About a Population Mean 340 The Essentials of the Test 340 Calculating the p-Value 344 Two Types of Errors 348 The Power of a Statistical Test 349 Exercises  352 9.3 A Large-Sample Test of Hypothesis for the ­Difference Between Two Population Means 354 Hypothesis Testing and Confidence Intervals 356 Exercises  357 9.4 A Large-Sample Test of Hypothesis for a Binomial Proportion 360 Statistical Significance and Practical Importance 362 Exercises  363 9.5 A Large-Sample Test of Hypothesis for the ­Difference Between Two Binomial Proportions 365 Exercises  367 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Contents ix 9.6 Concluding Comments on Testing Hypotheses 369 Chapter Review 370 Technology Today 371 Reviewing What You’ve Learned 375 Case Study: An Aspirin a Day... ? 378 10 Inference from Small Samples 380 Introduction 381 10.1 Student’s t Distribution 381 Assumptions behind Student’s t Distribution 384 Exercises  385 10.2 Small-Sample Inferences Concerning a Population Mean 386 Exercises  390 10.3 Small-Sample Inferences for the Difference Between Two Population Means: Independent Random Samples 394 Exercises  400 10.4 Small-Sample Inferences for the Difference Between Two Means: A Paired-­ Difference Test 404 Exercises  409 10.5 Inferences Concerning a Population Variance 413 Exercises  419 10.6 Comparing Two Population Variances 421 Exercises  427 10.7 Revisiting the Small-Sample Assumptions 429 Chapter Review 430 Technology Today 431 Reviewing What You’ve Learned 439 Case Study: School Accountability—Are We Doing Better? 443 11 The Analysis of Variance 445 11.1 The Design of an Experiment 446 Basic Definitions 446 What Is an Analysis of Variance? 447 The Assumptions for an Analysis of Variance 448 Exercises  448 11.2 The Completely Randomized Design: A One-Way Classification 449 Partitioning the Total Variation in the Experiment 450 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. x Contents Testing the Equality of the Treatment Means 453 Estimating Differences in the Treatment Means 455 Exercises  458 11.3 Ranking Population Means 461 Exercises  464 11.4 The Randomized Block Design: A Two-Way Classification 465 Partitioning the Total Variation in the Experiment 466 Testing the Equality of the Treatment and Block Means 469 Identifying Differences in the Treatment and Block Means 471 Some Cautionary Comments on Blocking 472 Exercises  473 11.5 The a 3 b Factorial Experiment: A Two-Way Classification 477 The Analysis of Variance for an a 3 b Factorial Experiment 479 Exercises  483 11.6 Revisiting the Analysis of Variance Assumptions 486 Residual Plots 487 11.7 A Brief Summary 489 Chapter Review 490 Technology Today 490 Reviewing What You’ve Learned 497 Case Study: How to Save Money on Groceries! 502 12 Simple Linear Regression and Correlation 503 Introduction 504 12.1 Simple Linear Regression 504 A Simple Linear Model 505 The Method of Least Squares 507 Exercises  509 12.2 An Analysis of Variance for Linear Regression 511 Exercises  514 12.3 Testing the Usefulness of the Linear ­Regression Model 516 Inferences About b, the Slope of the Line of Means 516 The Analysis of Variance F-Test 519 Measuring the Strength of the Relationship: The Coefficient of Determination 520 Interpreting the Results of a Significant Regression 521 Exercises  522 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Contents xi 12.4 Diagnostic Tools for Checking the Regression Assumptions 525 Dependent Error Terms 525 Residual Plots 525 Exercises  526 12.5 Estimation and Prediction Using the Fitted Line 530 Exercises  534 12.6 Correlation Analysis 537 Exercises  540 Chapter Review 543 Technology Today 544 Reviewing What You’ve Learned 549 Case Study: Is Your Car “Made in the U.S.A.”? 553 13 Multiple Linear Regression Analysis 555 Introduction 556 13.1 The Multiple Regression Model 556 13.2 Multiple Regression Analysis 558 The Method of Least Squares 558 The Analysis of Variance 559 Testing the Usefulness of the Regression Model 561 Interpreting the Results of a Significant Regression 562 Best Subsets Regression 563 Checking the Regression Assumptions 564 Using the Regression Model for Estimation and Prediction 564 Exercises  565 13.3 A Polynomial Regression Model 567 Exercises  570 13.4 Using Quantitative and Qualitative Predictor Variables in a Regression ­Model 573 Exercises  578 13.5 Testing Sets of Regression Coefficients 582 13.6 Other Topics in Multiple Linear Regression 584 Interpreting Residual Plots 584 Stepwise Regression Analysis 586 Binary Logistic Regression 587 Misinterpreting a Regression Analysis 587 13.7 Steps to Follow When Building a Multiple Regression Model 589 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. xii Contents Chapter Review 589 Technology Today 590 Reviewing What You’ve Learned 592 Case Study: “Made in the U.S.A.”—Another Look 598 14 Analysis of Categorical Data 599 14.1 The Multinomial Experiment and the Chi-Square Statistic 600 14.2 Testing Specified Cell Probabilities: The Goodness-of-Fit Test 602 Exercises  604 14.3 Contingency Tables: A Two-Way Classification 606 The Chi-Square Test of Independence 607 Exercises  611 14.4 Comparing Several Multinomial Populations: A Two-Way Classification with Fixed Row or Column Totals 614 Exercises  616 14.5 Other Topics in Categorical Data Analysis 619 The Equivalence of Statistical Tests 619 Other Applications of the Chi-Square Test 620 Chapter Review 621 Technology Today 622 Reviewing What You’ve Learned 627 Case Study: Who Is the Primary Breadwinner in Your Family? 631 15 Nonparametric Statistics 633 Introduction 634 15.1 The Wilcoxon Rank Sum Test: Independent Random Samples 634 Normal Approximation for the Wilcoxon Rank Sum Test 638 Exercises  641 15.2 The Sign Test for a Paired Experiment 643 Normal Approximation for the Sign Test 644 Exercises  646 15.3 A Comparison of Statistical Tests 648 15.4 The Wilcoxon Signed-Rank Test for a Paired Experiment 648 Normal Approximation for the Wilcoxon Signed-Rank Test 652 Exercises  653 15.5 The Kruskal–Wallis H-Test for Completely ­Randomized Designs 655 Exercises  658 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Contents xiii 15.6 The Friedman Fr-Test for Randomized Block Designs 660 Exercises  663 15.7 Rank Correlation Coefficient 666 Exercises  670 15.8 Summary 672 Chapter Review 672 Technology Today 673 Reviewing What You’ve Learned 676 Case Study: Amazon HQ2 680 Appendix I 681 Table 1 Cumulative Binomial Probabilities  682 Table 2 Cumulative Poisson Probabilities  688 Table 3 Areas under the Normal Curve  690 Table 4 Critical Values of t  692 Table 5 Critical Values of Chi-Square  694 Table 6 Percentage Points of the F Distribution  696 Table 7 Critical Values of T for the Wilcoxon Rank Sum Test, n1 # n2  704 Table 8 Critical Values of T for the Wilcoxon Signed-Rank Test, n 5 5(1)50  706 Table 9 Critical Values of Spearman’s Rank Correlation Coefficient for a One-Tailed Test  707 Table 10 Random Numbers  708 Table 11 Percentage Points of the Studentized Range, q.05(k, df )  710 Data Sources 714 Answers to Selected Exercises 727 Index 745 Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  Preface Every time you pick up a newspaper or a magazine, watch TV, or scroll through F ­ acebook, you encounter statistics. Every time you fill out a questionnaire, register at an online ­website, or pass your grocery rewards card through an electronic scanner, your personal information becomes part of a database containing your personal statistical information. You can’t avoid it! In this digital age, data collection and analysis are part of our day-to-day activities. If you want to be an educated consumer and citizen, you need to understand how statistics are used and misused in our daily lives. This international metric version is designed for classrooms and students outside of the United States. The units of measurement used in selected examples and exercises have been changed from U.S. Customary units to metric units. We did not update problems that are specific to U.S. Customary units, such as passing yards in football or data ­related to specific publications. The Secret to Our Success The first college course in introductory statistics that we ever took used Introduction to Probability and Statistics by William Mendenhall. Since that time, this text—currently in the fifteenth edition—has helped generations of students understand what statistics is all about and how it can be used as a tool in their particular area of application. The secret to the success of Introduction to Probability and Statistics is its ability to blend the old with the new. With each revision we try to build on the strong points of previous editions, and to look for new ways to motivate, encourage, and interest students using new technologies. Hallmark Features of the Fifteenth Edition The fifteenth edition keeps the traditional outline for the coverage of descriptive and ­inferential statistics used in previous editions. This revision maintains the straightforward presentation of the fourteenth edition. We have continued to simplify the language in order to make the text more readable—without sacrificing the statistical integrity of the presentation. We want students to understand how to apply statistical procedures, and also to understand how to meaningfully describe real sets of data how to explain the results of statistical tests in a practical way how to tell whether the assumptions behind statistical tests are valid what to do when these assumptions have been violated Exercises As with all previous editions, the variety and number of real applications in the exercise sets is a major strength of this edition. We have revised the exercise sets to provide new and xv Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. xvi Preface interesting real-world situations and real data sets, many of which are drawn from current periodicals and journals. The fifteenth edition contains over 1900 exercises, many of which are new to this edition. Exercises are graduated in level of difficulty; some, involving only basic techniques, can be solved by almost all students, while others, involving practical applications and interpretation of results, will challenge students to use more sophisticated statistical reasoning and understanding. Exercises have been rearranged to provide a more even distribution of exercises within each chapter and a new numbering system has been introduced, so that numbering begins again with each new section. Organization and Coverage We believe that Chapters 1 through 10—with the possible exception of Chapter 3—should be covered in the order presented. The remaining chapters can be covered in any order. The analysis of variance chapter precedes the regression chapter, so that the instructor can present the analysis of variance as part of a regression analysis. Thus, the most effective presentation would order these three chapters as well. Chapters 1–3 present descriptive data analysis for both one and two variables, using MINITAB 18, Microsoft Excel 2016®, and TI-83/84 Plus graphics. Chapter 4 includes a full presentation of probability. The last section of Chapter 4 in the fourteenth edition of the text, “Discrete Random Variables and Their Probability Distributions” has been moved to become the first section in Chapter 5. As in the fourteenth edition, the chapters on analysis of variance and linear regression include both calculational formulas and computer print- outs in the basic text presentation. These chapters can be used with equal ease by instructors who wish to use the ­“hands-on” computational approach to linear regression and ANOVA and by those who choose to ­focus on the interpretation of computer-generated statistical printouts. This edition includes ­expanded coverage of the uniform and exponential distri- butions in Chapter 5 and normal probability plots for assessing normality in Chapter 7, in ­addition to an expanded t-table (Table 4 in ­Appendix I). New topics in Chapter 13 ­include best subsets regression procedures and binary logistic regression. One important feature in the hypothesis testing chapters involves the emphasis on p-values and their use in judging statistical significance. With the advent of computer-­ generated p-values, these probabilities have become essential in reporting the results of a statistical analysis. As such, the observed value of the test statistic and its p-value are pre- sented together at the outset of our discussion of statistical hypothesis testing as equivalent tools for decision-making. Statistical significance is defined in terms of preassigned values of , and the p-value approach is presented as an alternative to the critical value approach for testing a statistical hypothesis. Examples are presented using both the p-value and ­critical value approaches to hypothesis testing. Discussion of the practical interpretation of statistical results, along with the difference between statistical significance and practical significance, is emphasized in the practical examples in the text. Special Features of the Fifteenth Edition NEED TO KNOW...: This edition again includes highlighted sections called “NEED TO KNOW...” and identified by this icon. These sections provide in- formation consisting of definitions, procedures, or step-by-step hints on problem solv- ing for specific questions such as “NEED TO KNOW… How to ­Construct a Relative Frequency Histogram?” or “NEED TO KNOW… How to Decide Which Test to Use?” Graphical and numerical data description includes both traditional and EDA ­methods, using computer graphics generated by MINITAB 18 for Windows and MS Excel 2016. Calculator screen captures from the TI-84 Plus calculator have been used for several examples, allowing students to access this option for data analysis. Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  42.5to use. Many researchers report you wish 30.0the smallest possible significance level for Ford Escape which41.5 28.0 their results are statistically significant. Empirical Rule should work relatively well. That is, Hyundai Tucson 41.5 28.0 approximately 68% of the measurements will fall between 16.1 Jeep Cherokee For example, 43.5 the TI-84 plus output for Example 30.0 9.7 (Figure 9.9) shows z 5 0.9090909091 Jeep Compass with p-value41.5 5 0.182. Detailed instructions for28.0the TI-83/84 plus as well as MINITAB can approximately be 95% of the measurements will fall between 10.6 Jeep Patriot found in the41.0 Technology Today section at the26.0end of this chapter. These results are consistent Preface approximately 99.7% of the measurements will xvii fall between 5.1 Kia Sportage with our hand 41.5calculations to the second decimal 28.0 place. Based on this p-value, H 0 cannot Mazda C-5 be rejected.42.0 The results are not statistically 27.5 significant. Toyota RAV4 42.0 30.0 Figure 2.11 6/25 Figure 9.9 Volkswagen Tiguan TI-84 plus output for 42.0 28.0 Relative frequency histogram for Example 2.8 Relative Frequency Example 9.7 4/25 1. Since the data involve two variables and a third labeling variable, enter the data into the first three columns of an Excel spreadsheet, using the labels in the table. Select Data ➤ Data Analysis ➤ Descriptive Statistics, and click OK. Highlight or type the Input 2/25 range (the data in the second and third columns) into the Descriptive Statistics Dialog box (Figure 2.19(a)). Type an Output location, make sure the boxes for “Labels in First 0 Row” and “Summary Statistics” are both checked, and click OK. The summary statistics 8.5 14.5 20.5 26.5 32.5 Scores (Figure 2.19(b)) will appear in the selected location in your spreadsheet. (a) Sometimes it is easy to confuse the significance(b) level  with the p-value (or observed Using Tchebysheff’s Theorem and the Empirical Rule significance level). They are both probabilities calculated as areas in the tails of the sampling distribution of the test statistic. However, the significance level  is preset by the experi- menter before collecting the data. The p-value is linked directly to the data and actually describes how likely or unlikely the sample results are, assuming that H 0 is true. The smaller Tchebysheff’s Theorem gives a lower bound the p-value, the more unlikely it is that H 0 is true! interval x 6 ks. At least 1 2 (1/k 2 ) probably more! ? Need to Know… Rejection Regions, p-Values, and Conclusions distribution). The significance level, a , lets you set the risk that you are willing to take of making an incorrect decision in a test of hypothesis. To set a rejection region, choose a critical value of z so that the area in the mate of the fraction of measurements falling within 1, 2, or 3 tail(s) of the z distribution is (are) either  for a one-tailed test or a /2 for a mean. two-tailed test. Use the right tail for an upper-tailed test and the left tail for a lower-tailed test. Reject H 0 when the test statistic exceeds the critical value 2. You may notice that some ofand the cells in the spreadsheet are overlapping. To adjust falls Allinexamples the rejectionand this, highlight the affected columns and click the Home tab. In the Cells group, exercises in the text that contain region. printouts or calculator Approximating screen s Using the Range To find choose Format ➤ AutoFit Column a p-value,are ­captures Width. find based You the area in