Statistics : principles and methods

Johnson provides a comprehensive, accurate introduction to statistics for business professionals who need to learn how to apply key concepts. The chapters have been updated with real-world data to make the material more relevant. The revised pedagogy will help them contextualize statistical concepts and procedures. The numerous examples clearly demonstrate the important points of the methods. New __What Will We Learn__ opening paragraphs set the stage for the material being discussed. __Using Statistics Wisely__ boxes summarize key lessons. In addition, __Statistics in Context__ sections give business professionals an understanding of applications in which a statistical approach to variation is needed. Cover Page 1 Title Page 5 Copyright Page 6 Preface 7 CONTENTS 13 1 INTRODUCTION 21 1 What Is Statistics? 23 2 Statistics in Our Everyday Life 23 3 Statistics in Aid of Scientific Inquiry 25 4 Two Basic Concepts—Population and Sample 28 5 The Purposeful Collection of Data 34 6 Statistics in Context 35 7 Objectives of Statistics 37 8 Using Statistics Wisely 38 9 Key Ideas 38 10 Review Exercises 39 2 ORGANIZATION AND DESCRIPTION OF DATA 41 1 Introduction 43 2 Main Types of Data 43 3 Describing Data by Tables and Graphs 44 3.1 Categorical Data 44 3.2 Discrete Data 48 3.3 Data on a Continuous Variable 49 4 Measures of Center 60 5 Measures of Variation 68 6 Checking the Stability of the Observations over Time 80 7 More on Graphics 84 8 Statistics in Context 86 9 Using Statistics Wisely 88 10 Key Ideas and Formulas 88 11 Technology 90 12 Review Exercises 93 3 DESCRIPTIVE STUDY OF BIVARIATE DATA 101 1 Introduction 103 2 Summarization of Bivariate Categorical Data 103 3 A Designed Experiment for Making a Comparison 108 4 Scatter Diagram of Bivariate Measurement Data 110 5 The Correlation Coefficient—A Measure of Linear Relation 113 6 Prediction of One Variable from Another (Linear Regression) 124 7 Using Statistics Wisely 129 8 Key Ideas and Formulas 129 9 Technology 130 10 Review Exercises 131 4 PROBABILITY 135 1 Introduction 137 2 Probability of an Event 138 3 Methods of Assigning Probability 144 3.1 Equally Likely Elementary Outcomes— The Uniform Probability Model 144 3.2 Probability As the Long-Run Relative Frequency 146 4 Event Relations and Two Laws of Probability 152 5 Conditional Probability and Independence 161 6 Bayes’ Theorem 169 7 Random Sampling from a Finite Population 175 8 Using Statistics Wisely 182 9 Key Ideas and Formulas 182 10 Technology 184 11 Review Exercises 185 5 PROBABILITY DISTRIBUTIONS 191 1 Introduction 193 2 Random Variables 193 3 Probability Distribution of a Discrete Random Variable 196 4 Expectation (Mean) and Standard Deviation of a Probability Distribution 205 5 Successes and Failures—Bernoulli Trials 213 6 The Binomial Distribution 218 7 The Binomial Distribution in Context 228 8 Using Statistics Wisely 231 9 Key Ideas and Formulas 232 10 Technology 233 11 Review Exercises 235 6 THE NORMAL DISTRIBUTION 241 1 Probability Model for a Continuous Random Variable 243 2 The Normal Distribution—Its General Features 250 3 The Standard Normal Distribution 253 4 Probability Calculations with Normal Distributions 258 5 The Normal Approximation to the Binomial 262 *6 Checking the Plausibility of a Normal Model 268 *7 Transforming Observations to Attain Near Normality 271 8 Using Statistics Wisely 274 9 Key Ideas and Formulas 275 10 Technology 276 11 Review Exercises 277 7 VARIATION IN REPEATED SAMPLES— SAMPLING DISTRIBUTIONS 283 1 Introduction 285 2 The Sampling Distribution of a Statistic 286 3 Distribution of the Sample Mean and the Central Limit Theorem 293 4 Statistics in Context 305 5 Using Statistics Wisely 309 6 Key Ideas and Formulas 309 7 Review Exercises 310 8 Class Projects 312 9 Computer Project 313 8 DRAWING INFERENCES FROM LARGE SAMPLES 315 1 Introduction 317 2 Point Estimation of a Population Mean 319 3 Confidence Interval for a Population Mean 325 4 Testing Hypotheses about a Population Mean 334 5 Inferences about a Population Proportion 349 6 Using Statistics Wisely 357 7 Key Ideas and Formulas 358 8 Technology 360 9 Review Exercises 363 9 SMALL-SAMPLE INFERENCESFOR NORMAL POPULATIONS 369 1 Introduction 371 2 Student’s t Distribution 371 3 Inferences about μ—Small Sample Size 375 3.1 Confidence Interval for μ 375 3.2 Hypotheses Tests for μ 378 4 Relationship between Tests and Confidence Intervals 383 5 Inferences about the Standard Deviation σ (The Chi-Square Distribution) 386 6 Robustness of Inference Procedures 391 7 Using Statistics Wisely 392 8 Key Ideas and Formulas 393 9 Technology 395 10 Review Exercises 396 10 COMPARING TWO TREATMENTS 401 1 Introduction 403 2 Independent Random Samples from Two Populations 406 3 Large Samples Inference about Difference of Two Means 408 4 Inferences from Small Samples: Normal Populations with Equal Variances 414 5 Inferences from Small Samples: Normal Populations with Unequal Variances 420 5.1 A Conservative t Test 420 5.2 An Approximate t Test—Satterthwaite Correction 422 6 Randomization and Its Role in Inference 427 7 Matched Pairs Comparisons 429 7.1 Inferences from a Large Number of Matched Pairs 432 7.2 Inferences from a Small Number of Matched Pairs 433 7.3 Randomization with Matched Pairs 436 8 Choosing between Independent Samples and a Matched Pairs Sample 438 9 Comparing Two Population Proportions 440 10 Using Statistics Wisely 446 11 Key Ideas and Formulas 447 12 Technology 451 13 Review Exercises 454 11 REGRESSION ANALYSIS—I Simple Linear Regression 459 1 Introduction 461 2 Regression with a Single Predictor 463 3 A Straight-Line Regression Model 466 4 The Method of Least Squares 468 5 The Sampling Variability of the Least Squares Estimators— Tools for Inference 476 6 Important Inference Problems 478 6.1. Inference Concerning the Slope β1 478 6.2. Inference about the Intercept β0 480 6.3. Estimation of the Mean Response for a Specified x Value 480 6.4. Prediction of a Single Response for a Specified x Value 483 7 The Strength of a Linear Relation 491 8 Remarks about the Straight Line Model Assumptions 496 9 Using Statistics Wisely 496 10 Key Ideas and Formulas 497 11 Technology 500 12 Review Exercises 501 12 REGRESSION ANALYSIS—II Multiple Linear Regression and Other Topics 505 1 Introduction 507 2 Nonlinear Relations and Linearizing Transformations 507 3 Multiple Linear Regression 511 4 Residual Plots to Check the Adequacy of a Statistical Model 523 5 Using Statistics Wisely 527 6 Key Ideas and Formulas 527 7 Technology 528 8 Review Exercises 529 13 ANALYSIS OF CATEGORICAL DATA 533 1 Introduction 535 2 Pearson’s χ2 Test for Goodness of Fit 538 3 Contingency Table with One Margin Fixed (Test of Homogeneity) 542 4 Contingency Table with Neither Margin Fixed (Test of Independence) 551 5 Using Statistics Wisely 557 6 Key Ideas and Formulas 557 7 Technology 559 8 Review Exercises 560 14 ANALYSIS OF VARIANCE (ANOVA) 563 1 Introduction 565 2 Comparison of Several Treatments— The Completely Randomized Design 565 3 Population Model and Inferences for a Completely Randomized Design 573 4 Simultaneous Confidence Intervals 577 5 Graphical Diagnostics and Displays to Supplement ANOVA 581 6 Randomized Block Experiments for Comparing k Treatments 583 7 Using Statistics Wisely 591 8 Key Ideas and Formulas 592 9 Technology 593 10 Review Exercises 594 15 NONPARAMETRIC INFERENCE 597 1 Introduction 599 2 The Wilcoxon Rank-Sum Test for Comparing Two Treatments 599 3 Matched Pairs Comparisons 610 4 Measure of Correlation Based on Ranks 619 5 Concluding Remarks 623 6 Using Statistics Wisely 624 7 Key Ideas and Formulas 624 8 Technology 625 9 Review Exercises 625 APPENDICES 629 A1 Summation Notation 629 A2 Rules for Counting 634 A3 Expectation and Standard Deviation - Properties 637 A4 The Expected Value and Standard Deviation of X_bar 642 B Tables 644 Table 1 Random Digits 644 Table 2 Cumulative Binomial Probabilities 647 Table 3 Standard Normal Probabilities 654 Table 4 Percentage Points of t Distributions 656 Table 5 Percentage Points of χ2 Distributions 657 Table 6 Percentage Points of F (μ1, μ2) Distributions 658 Table 7 Selected Tail Probabilities for the Null Distribution of Wilcoxon’s Rank-Sum Statistic 660 Table 8 Selected Tail Probabilities for the Null Distribution of Wilcoxon’s Signed-Rank Statistic 665 Data Bank (Table D) 667 Answers to Selected Odd-Numbered Exercises 685 INDEX 701 3. Distribution of the Sample Mean and the Central Limit Theorem 4. Statistics in Context 8. Drawing Inferences From Large Samples 1. Introduction 2. Point Estimation of Population Mean 3. Confidence Interval for a Population Mean 4. Testing Hypotheses about a Population Mean 5. Inferences about a Population Proportion 9. Small-Sample Inferences for Normal Populations 1. Introduction 2. Student's t Distribution 3. Inferences about ©Œ -Small Sample Size 4. Relationship between Tests and Confidence Intervals 5. Inferences About the Standard Deviation o (The Chi-Square Distribution) 6. Robustness of Inference Procedures 10. Comparing Two Treatments 1. Introduction 2. Independent Random Samples from Two Populations 3. Large Samples Inference about Difference of Two Means 4. Inferences from Small Samples: Normal Populations with Equal Variances 5. Inferences from Small Samples: Normal Populations but Unequal Variances 6. Randomization and its Role in Inference 7. Matched Pairs Comparisons 8. Choosing Between Independent Samples and a Matched Pairs Sample 9. Comparing Two Population Proportions 11. Regression Analysis I (Simple Linear Regression) 1. Introduction 2. Regression with a Single Predictor 3. A Straight-Line Regression Model 4. The Method of Least Squares 5. The Sampling Variability of the Least Squares Estimators Tools for Inference 6. Important Inference Problems 7. The Strength of a Linear Relation 8. Remarks About the Straight Line Model Assumption 12. Regression Analysis- II Multiple Linear Regression and Other Topics 1. Introduction 2. Nonlinear Relations and Linearizing Transformations 3. Multiple Linear Regression 4. Residual Plots to Check the Adequacy of a Statistical Model 5. Review Exercises 13. Analysis of Categorical Data 1. Introduction 2. Pearson's x 2 Test for Goodness of Fit 3. Contingency Table with One Margin Fixed (Test of Homogeneity). Johnson provides a comprehensive, accurate introduction to statistics for business professionals who need to learn how to apply key concepts. The chapters have been updated with real-world data to make the material more relevant. The revised pedagogy will help them contextualize statistical concepts and procedures. The numerous examples clearly demonstrate the important points of the methods. New What Will We Learn opening paragraphs set the stage for the material being discussed. Using Statistics Wisely boxes summarize key lessons. In addition, Statistics in Context sections give business professionals an understanding of applications in which a statistical approach to variation is needed. * Johnson/Bhattacharyya is unique in its clarity of expositionwhile maintaining the mathematical correctness of itsexplanations. * This highly regarded text provides a wide range of contemporaryapplications in its examples and exercises. * The chapters have been updated with real-world data to make thematerial more relevant.