Introductory Statistics

Description

Introductory Statistics, Third Edition, presents statistical concepts and techniques in a manner that will teach students not only how and when to utilize the statistical procedures developed, but also to understand why these procedures should be used. This book offers a unique historical perspective, profiling prominent statisticians and historical events in order to motivate learning. To help guide students towards independent learning, exercises and examples using real issues and real data (e.g., stock price models, health issues, gender issues, sports, scientific fraud) are provided. The chapters end with detailed reviews of important concepts and formulas, key terms, and definitions that are useful study tools. Data sets from text and exercise material are available for download in the text website. This text is designed for introductory non-calculus based statistics courses that are offered by mathematics and/or statistics departments to undergraduate students taking a semester course in basic Statistics or a year course in Probability and Statistics. Cover Page......Page 1 Title Page......Page 4 Copyright Page......Page 5 ABOUT THE AUTHOR......Page 6 DEDICATION......Page 7 PREFACE......Page 18 ACKNOWLEDGMENTS......Page 22 Contents......Page 8 1.1 Introduction......Page 24 1.2.1 Data Collection......Page 26 1.2.2 Inferential Statistics and Probability Models......Page 27 1.3 Populations and Samples......Page 28 1.3.1 Stratified Random Sampling......Page 29 1.4 A Brief History of Statistics......Page 30 Key Terms......Page 33 Review Problems......Page 34 Chapter 2 Describing Data Sets......Page 40 2.2 Frequency Tables and Graphs......Page 41 2.2.1 Line Graphs, Bar Graphs, and Frequency Polygons......Page 42 2.2.2 Relative Frequency Graphs......Page 44 2.2.3 Pie Charts......Page 47 Problems......Page 48 2.3 Grouped Data and Histograms......Page 55 Problems......Page 62 2.4 Stem-and-Leaf Plots......Page 67 Problems......Page 70 2.5 Sets of Paired Data......Page 74 Problems......Page 77 2.6 Some Historical Comments......Page 81 Key Terms......Page 82 Summary......Page 83 Review Problems......Page 86 Chapter 3 Using Statistics to Summarize Data Sets......Page 94 3.1 Introduction......Page 95 3.2 Sample Mean......Page 96 3.2.1 Deviations......Page 101 Problems......Page 102 3.3 Sample Median......Page 106 Problems......Page 109 3.3.1 Sample Percentiles......Page 113 3.4 Sample Mode......Page 120 Problems......Page 121 3.5 Sample Variance and Sample Standard Deviation......Page 122 Problems......Page 128 3.6 Normal Data Sets and the Empirical Rule......Page 132 Problems......Page 137 3.7 Sample Correlation Coefficient......Page 143 Problems......Page 151 Key Terms......Page 157 Summary......Page 159 Review Problems......Page 161 Chapter 4 Probability......Page 168 4.2 Sample Space and Events of an Experiment......Page 169 Problems......Page 173 4.3 Properties of Probability......Page 176 Problems......Page 179 4.4 Experiments Having Equally Likely Outcomes......Page 184 Problems......Page 187 4.5 Conditional Probability and Independence......Page 190 Problems......Page 200 4.6 Bayes’ Theorem......Page 208 Problems......Page 210 4.7 Counting Principles......Page 212 Problems......Page 218 Key Terms......Page 221 Summary......Page 223 Review Problems......Page 224 Chapter 5 Discrete Random Variables......Page 232 5.1 Introduction......Page 233 5.2 Random Variables......Page 234 Problems......Page 238 5.3 Expected Value......Page 241 5.3.1 Properties of Expected Values......Page 244 Problems......Page 248 5.4 Variance of Random Variables......Page 254 5.4.1 Properties of Variances......Page 256 Problems......Page 259 5.5 Binomial Random Variables......Page 261 5.5.1 Expected Value and Variance of a Binomial Random Variable......Page 266 Problems......Page 267 5.6 Hypergeometric Random Variables......Page 271 Problems......Page 272 5.7 Poisson Random Variables......Page 273 Problems......Page 276 Summary......Page 277 Review Problems......Page 279 Chapter 6 Normal Random Variables......Page 284 6.2 Continuous Random Variables......Page 285 Problems......Page 287 6.3 Normal Random Variables......Page 289 Problems......Page 292 6.4 Probabilities Associated with a Standard Normal Random Variable......Page 294 Problems......Page 299 6.5 Finding Normal Probabilities: Conversion to the Standard Normal......Page 300 6.6 Additive Property of Normal Random Variables......Page 302 Problems......Page 304 6.7 Percentiles of Normal Random Variables......Page 307 Problems......Page 312 Summary......Page 313 Review Problems......Page 316 Chapter 7 Distributions of Sampling Statistics......Page 320 7.2 Introduction......Page 321 7.3 Sample Mean......Page 322 Problems......Page 326 7.4 Central Limit Theorem......Page 327 7.4.1 Distribution of the Sample Mean......Page 329 7.4.2 How Large a Sample Is Needed?......Page 333 Problems......Page 334 7.5 Sampling Proportions from a Finite Population......Page 336 7.5.1 Probabilities Associated with Sample Proportions: The Normal Approximation to the Binomial Distribution......Page 340 Problems......Page 342 7.6 Distribution of the Sample Variance of a Normal Population......Page 346 Key Terms......Page 348 Summary......Page 349 Review Problems......Page 350 Chapter 8 Estimation......Page 354 8.1 Introduction......Page 355 8.2 Point Estimator of a Population Mean......Page 356 Problems......Page 357 8.3 Point Estimator of a Population Proportion......Page 359 Problems......Page 361 8.3.1 Estimating the Probability of a Sensitive Event......Page 364 8.4 Estimating a Population Variance......Page 365 Problems......Page 367 8.5 Interval Estimators of the Mean of a Normal Population with Known Population Variance......Page 370 8.5.1 Lower and Upper Confidence Bounds......Page 378 Problems......Page 380 8.6 Interval Estimators of the Mean of a Normal Population with Unknown Population Variance......Page 382 8.6.1 Lower and Upper Confidence Bounds......Page 387 Problems......Page 389 8.7 Interval Estimators of a Population Proportion......Page 394 8.7.1 Length of the Confidence Interval......Page 396 8.7.2 Lower and Upper Confidence Bounds......Page 398 Problems......Page 400 Key Terms......Page 403 Summary......Page 404 Review Problems......Page 406 Chapter 9 Testing Statistical Hypotheses......Page 410 9.2 Hypothesis Tests and Significance Levels......Page 411 Problems......Page 415 9.3 Tests Concerning the Mean of a Normal Population: Case of Known Variance......Page 417 Problems......Page 423 9.3.1 One-Sided Tests......Page 426 9.4 The t Test for the Mean of a Normal Population: Case of Unknown Variance......Page 432 Problems......Page 440 9.5 Hypothesis Tests Concerning Population Proportions......Page 444 9.5.1 Two-Sided Tests of p......Page 448 Problems......Page 452 Summary......Page 456 Review Problems and Proposed Case Studies......Page 460 Chapter 10 Hypothesis Tests Concerning Two Populations......Page 466 10.1 Introduction......Page 467 10.2 Testing Equality of Means of Two Normal Populations: Case of Known Variance......Page 469 Problems......Page 473 10.3 Testing Equality of Means: Unknown Variances and Large Sample Sizes......Page 476 Problems......Page 482 10.4 Testing Equality of Means: Small-Sample Tests When the Unknown Population Variances Are Equal......Page 486 Problems......Page 491 10.5 Paired-Sample t Test......Page 494 Problems......Page 499 10.6 Testing Equality of Population Proportions......Page 504 Problems......Page 513 Summary......Page 516 Review Problems......Page 521 Chapter 11 Analysis of Variance......Page 526 11.1 Introduction......Page 527 11.2 One-Factor Analysis of Variance......Page 528 A Remark on the Degrees of Freedom......Page 530 Problems......Page 533 11.3 Two-Factor Analysis of Variance: Introduction and Parameter Estimation......Page 537 Problems......Page 541 11.4 Two-Factor Analysis of Variance: Testing Hypotheses......Page 543 Problems......Page 550 11.5 Final Comments......Page 552 Summary......Page 553 Review Problems......Page 556 Chapter 12 Linear Regression......Page 560 12.1 Introduction......Page 562 12.2 Simple Linear Regression Model......Page 563 Problems......Page 565 12.3 Estimating the Regression Parameters......Page 567 Problems......Page 571 12.4 Error Random Variable......Page 576 Problems......Page 579 12.5 Testing the Hypothesis that ß = 0......Page 580 Problems......Page 583 12.6 Regression to the Mean......Page 587 12.6.1 Why Biological Data Sets Are Often Normally Distributed......Page 592 Problems......Page 593 12.7 Prediction Intervals for Future Responses......Page 596 Problems......Page 598 12.8 Coefficient of Determination......Page 601 Problems......Page 603 12.9 Sample Correlation Coefficient......Page 605 Problems......Page 606 12.10 Analysis of Residuals: Assessing the Model......Page 607 12.11 Multiple Linear Regression Model......Page 609 12.11.1 Dummy Variables for Categorical Data......Page 613 Problems......Page 615 Summary......Page 618 Review Problems......Page 622 Chapter 13 Chi-Squared Goodness-of-Fit Tests......Page 628 13.1 Introduction......Page 629 13.2 Chi-Squared Goodness-of-Fit Tests......Page 632 Problems......Page 638 13.3 Testing for in Dependence in Populations Classified According to Two Characteristics......Page 643 Problems......Page 649 13.4 Testing for Independence in Contingency Tables with Fixed Marginal Totals......Page 654 Problems......Page 657 Key Terms......Page 660 Summary......Page 661 Review Problems......Page 663 Chapter 14 Nonparametric Hypotheses Tests......Page 670 14.2 Sign Test......Page 671 14.2.1 Testing the Equality of Population Distributions when Samples Are Paired......Page 675 14.2.2 One-Sided Tests......Page 676 Problems......Page 678 14.3 Signed-Rank Test......Page 680 14.3.1 Zero Differences and Ties......Page 685 Problems......Page 687 14.4 Rank-Sum Test for Comparing Two Populations......Page 690 14.4.1 Comparing Nonparametric Tests with Tests that Assume Normal Distributions......Page 695 Problems......Page 696 14.5 Runs Test for Randomness......Page 699 Problems......Page 704 14.6 Testing the Equality of Multiple Probability Distributions......Page 706 14.6.1 When the Data Are a Set of Comparison Rankings......Page 708 Problems......Page 711 14.7 Permutation Tests......Page 712 Problems......Page 715 Summary......Page 716 Review Problems......Page 719 Chapter 15 Quality Control......Page 722 15.2 The X Control Chart for Detecting a Shift in the Mean......Page 723 Problems......Page 728 15.2.1 When the Mean and Variance Are Unknown......Page 730 15.2.2 S Control Charts......Page 733 Problems......Page 736 15.3 Control Charts for Fraction Defective......Page 738 15.4 Exponentially Weighted Moving-Average Control Charts......Page 740 Problems......Page 744 15.5 Cumulative-Sum Control Charts......Page 745 Summary......Page 748 Review Problems......Page 749 Appendices......Page 750 Appendix A. Data Set......Page 752 B.2 Absolute Value......Page 756 B.3 Set Notation......Page 757 Appendix C How to Choose a Random Sample......Page 758 Table D.1 Standard Normal Probabilities......Page 762 Table D.2 Percentiles tn,α of t Distributions......Page 763 Table D.3 Percentiles χ²n,α of the Chi-Squared Distributions......Page 764 Table D.4 Percentiles of F Distributions......Page 766 Table D.5 Binomial Distribution Function......Page 772 Appendix E. Programs......Page 778 Answers to Odd-Numbered Problems......Page 780 Index......Page 830