# Business Statistics: Communicating With Numbers, 3rd Edition PDF by Sanjiv Jaggia and Alison Kelly

## Business Statistics: Communicating With Numbers, Third Edition

By Sanjiv Jaggia and Alison Kelly Contents:

PART ONE

Introduction

CHAPTER 1

STATISTICS AND DATA 2

The Relevance of Statistics 4

What Is Statistics? 5

The Need for Sampling 6

Cross-Sectional and Time Series Data 6

Structured and Unstructured Data 7

Big Data 8

Data on the Web 8

Variables and Scales of Measurement 10

The Nominal Scale 11

The Ordinal Scale 12

The Interval Scale 13

The Ratio Scale 14

Synopsis of Introductory Case 15

Conceptual Review 16

PART TWO

Descriptive Statistics

CHAPTER 2

TABULAR AND GRAPHICAL METHODS 18

Summarizing Qualitative Data 20

Pie Charts and Bar Charts 21

Cautionary Comments When Constructing or Interpreting Charts or Graphs 24

Using Excel to Construct a Pie Chart and a Bar Chart 24

A Pie Chart 24

A Bar Chart 25

Using R to Construct a Pie Chart 25

Summarizing Quantitative Data 28

Guidelines for Constructing a Frequency Distribution 29

Synopsis of Introductory Case 33

Histograms, Polygons, and Ogives 33

Using Excel to Construct a Histogram, a Polygon, and an Ogive 37

A Histogram Constructed from Raw Data 37

A Histogram Constructed from a Frequency Distribution 38

A Polygon 39

An Ogive 39

Using R to Construct a Histogram, a Polygon, and an Ogive 39

A Histogram 39

A Polygon 40

An Ogive 40

Stem-and-Leaf Diagrams 45

Scatterplots 47

Using Excel and R to Construct a Scatterplot 48

Using Excel 48

Using R 49

Writing with Statistics 50

Conceptual Review 52

Additional Exercises and Case Studies 53

Exercises 53

Case Studies 56

Appendix 2.1: Guidelines for Other Software Packages 58

CHAPTER 3

NUMERICAL DESCRIPTIVE MEASURES 62

Measures of Central Location 64

The Mean 64

The Median 66

The Mode 67

The Weighted Mean 68

Using Excel and R to Calculate Measures of Central Location 69

Using Excel’s Formula Option 69

Using Excel’s Data Analysis Toolpak Option 70

Using R 71

Note on Symmetry 72

Percentiles and Boxplots 74

Calculating the pth Percentile 75

Note on Calculating Percentiles 76

Constructing and Interpreting a Boxplot 76

Using R to Construct a Boxplot 77

The Geometric Mean 79

The Geometric Mean Return 79

Arithmetic Mean versus Geometric Mean 80

The Average Growth Rate 81

Measures of Dispersion 83

Range 84

The Mean Absolute Deviation 84

The Variance and the Standard Deviation 85

The Coefficient of Variation 86

Using Excel and R to Calculate Measures of Dispersion 87

Using Excel’s Formula Option 87

Using Excel’s Data Analysis Toolpak Option 87

Using R 87

Mean-Variance Analysis and the Sharpe Ratio 89

Synopsis of Introductory Case 91

Analysis of Relative Location 92

Chebyshev’s Theorem 92

The Empirical Rule 93

z-Scores 94

Summarizing Grouped Data 97

Measures of Association 100

Using Excel and R to Calculate Measures of Association 102

Using Excel 102

Using R 102

Writing with Statistics 104

Conceptual Review 105

Additional Exercises and Case Studies 107

Exercises 107

Case Studies 110

Appendix 3.1: Guidelines for Other Software Packages 112

PART THREE

Probability and Probability Distributions

CHAPTER 4

INTRODUCTION TO PROBABILITY 114

Fundamental Probability Concepts 116

Events 117

Assigning Probabilities 119

Probabilities Expressed as Odds 122

Rules of Probability 125

The Complement Rule 125

The Addition Rule for Mutually Exclusive Events 127

Conditional Probability 128

Independent and Dependent Events 130

The Multiplication Rule 131

The Multiplication Rule for Independent Events 131

Contingency Tables and Probabilities 135

Synopsis of Introductory Case 138

The Total Probability Rule and Bayes’ Theorem 140

The Total Probability Rule 140

Bayes’ Theorem 143

Counting Rules 147

Writing with Statistics 150

Conceptual Review 151

Additional Exercises and Case Studies 153

Exercises 153

Case Studies 157

CHAPTER 5

DISCRETE PROBABILITY DISTRIBUTIONS 160

Random Variables and Discrete Probability Distributions 162

The Discrete Probability Distribution 163

Expected Value, Variance, and Standard Deviation 167

Expected Value 168

Variance and Standard Deviation 168

Risk Neutrality and Risk Aversion 169

Portfolio Returns 172

Properties of Random Variables 172

Expected Return, Variance, and Standard Deviation for a Portfolio 173

The Binomial Distribution 176

Using Excel and R to Obtain Binomial Probabilities 181

The Poisson Distribution 184

Synopsis of Introductory Case 187

Using Excel and R to Obtain Poisson Probabilities 187

The Hypergeometric Distribution 190

Using Excel and R to Obtain Hypergeometric Probabilities 192

Writing with Statistics 194

Conceptual Review 196

Additional Exercises and Case Studies 197

Exercises 197

Case Studies 200

Appendix 5.1: Guidelines for Other Software Packages 201

CHAPTER 6

CONTINUOUS PROBABILITY DISTRIBUTIONS 204

Continuous Random Variables and the Uniform Distribution 206

The Continuous Uniform Distribution 207

The Normal Distribution 210

Characteristics of the Normal Distribution 211

The Standard Normal Distribution 212

Finding a Probability for a Given z Value 213

Finding a z Value for a Given Probability 215

The Transformation of Normal Random Variables 217

Synopsis of Introductory Case 221

A Note on the Normal Approximation of the Binomial Distribution 221

Using Excel and R for the Normal Distribution 221

Other Continuous Probability Distributions 226

The Exponential Distribution 226

The Lognormal Distribution 229

Using Excel and R for the Exponential and Lognormal Distributions 231

Writing with Statistics 235

Conceptual Review 236

Additional Exercises and Case Studies 238

Exercises 238

Case Studies 240

Appendix 6.1: Guidelines for Other Software Packages 242

PART FOUR

Basic Inference

CHAPTER 7

SAMPLING AND SAMPLING DISTRIBUTIONS 246

Sampling 248

Classic Case of a “Bad” Sample: The Literary Digest Debacle of 1936 248

Trump’s Stunning Victory in 2016 249

Sampling Methods 250

Using Excel and R to Generate a Simple Random Sample 252

The Sampling Distribution of the Sample Mean 253

The Expected Value and the Standard Error of the Sample Mean 254

Sampling from a Normal Population 255

The Central Limit Theorem 257

The Sampling Distribution of the Sample Proportion 260

The Expected Value and the Standard Error of the Sample Proportion 260

Synopsis of Introductory Case 264

The Finite Population Correction Factor 265

Statistical Quality Control 268

Control Charts 269

Using Excel and R to Create a Control Chart 272

Writing with Statistics 276

Conceptual Review 277

Additional Exercises and Case Studies 279

Exercises 279

Case Studies 282

Appendix 7.1: Derivation of the Mean and the Variance for and 283

Sample Mean, 283

Sample Proportion, 283

Appendix 7.2: Properties of Point Estimators 283

Appendix 7.3: Guidelines for Other Software Packages 285

CHAPTER 8

INTERVAL ESTIMATION 288

Confidence Interval for the Population Mean When σ Is Known 290

Constructing a Confidence Interval for μ When σ Is Known 291

The Width of a Confidence Interval 293

Using Excel and R to Construct a Confidence Interval for μ When σ Is Known 295

Confidence Interval for the Population Mean When σ Is Unknown 298

The t Distribution 298

Summary of the tdf Distribution 299

Locating tdf Values and Probabilities 300

Constructing a Confidence Interval for μ When σ Is Unknown 301

Using Excel and R to Construct a Confidence Interval for μ When σ Is Unknown 302

Confidence Interval for the Population Proportion 307

Selecting the Required Sample Size 310

Selecting n to Estimate μ 310

Selecting n to Estimate p 311

Synopsis of Introductory Case 312

Writing with Statistics 314

Conceptual Review 315

Additional Exercises and Case Studies 316

Exercises 316

Case Studies 319

Appendix 8.1: Guidelines for Other Software Packages 321

CHAPTER 9

HYPOTHESIS TESTING 322

Introduction to Hypothesis Testing 324

The Decision to “Reject” or “Not Reject” the Null Hypothesis 324

Defining the Null and the Alternative Hypotheses 325

Type I and Type II Errors 327

Hypothesis Test for the Population Mean When σ Is Known 330

The p-Value Approach 330

Confidence Intervals and Two-Tailed Hypothesis Tests 334

Using Excel and R to Test μ When σ Is Known 335

One Last Remark 336

Hypothesis Test for the Population Mean When σ Is Unknown 339

Using Excel and R to Test μ When σ is Unknown 340

Synopsis of Introductory Case 342

Hypothesis Test for the Population Proportion 345

Writing with Statistics 348

Conceptual Review 350

Additional Exercises and Case Studies 351

Exercises 351

Case Studies 354

Appendix 9.1: The Critical Value Approach 356

Appendix 9.2: Guidelines for Other Software Packages 358

CHAPTER 10

STATISTICAL INFERENCE CONCERNING TWO POPULATIONS 360

Inference Concerning the Difference between Two Means 362

Confidence Interval for μ1 − μ2 362

Hypothesis Test for μ1 − μ2 364

Using Excel and R for Testing Hypotheses about μ1 − μ2 366

A Note on the Assumption of Normality 369

Inference Concerning Mean Differences 373

Recognizing a Matched-Pairs Experiment 374

Confidence Interval for μD 374

Hypothesis Test for μD 375

Using Excel and R for Testing Hypotheses about μD 377

One Last Note on the Matched-Pairs Experiment 379

Synopsis of Introductory Case 379

Inference Concerning the Difference between Two Proportions 382

Confidence Interval for p1 − p2 383

Hypothesis Test for p1 − p2 384

Writing with Statistics 389

Conceptual Review 390

Additional Exercises and Case Studies 392

Exercises 392

Case Studies 394

Appendix 10.1: Guidelines for Other Software Packages 396

CHAPTER 11

STATISTICAL INFERENCE CONCERNING VARIANCE 398

Inference Concerning the Population Variance 400

Sampling Distribution of S2 400

Finding χ2 df Values and Probabilities 401

Confidence Interval for the Population Variance 403

Hypothesis Test for the Population Variance 404

Note on Calculating the p-Value for a Two-Tailed Test Concerning σ2 405

Using Excel and R to Test σ2 405

Inference Concerning the Ratio of Two Population Variances 409

Sampling Distribution of S12 1/S2 2 409

Finding F(df1,df2) Values and Probabilities 410

Confidence Interval for the Ratio of Two Population Variances 412

Hypothesis Test for the Ratio of Two Population Variances 413

Using Excel and R to Test σ12⁄σ2 2 415

Synopsis of Introductory Case 416

Writing with Statistics 419

Conceptual Review 420

Additional Exercises and Case Studies 421

Exercises 421

Case Studies 423

Appendix 11.1: Guidelines for Other Software Packages 425

CHAPTER 12

CHI-SQUARE TESTS 426

Goodness-of-Fit Test for a Multinomial Experiment 428

Using R to Conduct a Goodness-of-Fit Test 432

Chi-Square Test for Independence 435

Calculating Expected Frequencies 436

Synopsis of Introductory Case 439

Using R to Conduct a Test for Independence 440

Chi-Square Tests for Normality 443

The Goodness-of-Fit Test for Normality 443

The Jarque-Bera Test 445

Using R to Conduct a Goodness-of-Fit Test for Normality and the Jarque-Bera

Test 446

Writing with Statistics 450

Conceptual Review 451

Additional Exercises and Case Studies 453

Exercises 453

Case Studies 457

Appendix 12.1: Guidelines for Other Software Packages 458

PART FIVE

CHAPTER 13

ANALYSIS OF VARIANCE 460

One-Way ANOVA Test 462

Between-Treatments Estimate of σ2: MSTR 463

Within-Treatments Estimate of σ2: MSE 464

The One-Way ANOVA Table 466

Using Excel and R to Construct a One-Way ANOVA Table 466

Multiple Comparison Methods 471

Fisher’s Least Significant Difference (LSD) Method 472

Synopsis of Introductory Case 473

Tukey’s Honestly Significant Difference (HSD) Method 474

Using R to Construct Tukey Confidence Intervals for μ1 − μ2 476

Two-Way ANOVA Test: No Interaction 480

The Sum of Squares for Factor A, SSA 482

The Sum of Squares for Factor B, SSB 483

The Error Sum of Squares, SSE 483

Using Excel and R for a Two-Way ANOVA Test— No Interaction 484

Two-Way ANOVA Test: With Interaction 489

The Total Sum of Squares, SST 490

The Sum of Squares for Factor A, SSA, and the Sum of Squares for Factor B, SSB 490

The Sum of Squares for the Interaction of Factor A and Factor B, SSAB 491

The Error Sum of Squares, SSE 492

Using Excel and R for a Two-Way ANOVA Test— With Interaction 492

Writing with Statistics 497

Conceptual Review 498

Additional Exercises and Case Studies 499

Case Studies 504

Appendix 13.1: Guidelines for Other Software Packages 506

CHAPTER 14

REGRESSION ANALYSIS 508

Hypothesis Test for the Correlation Coefficient 510

Testing the Correlation Coefficient ρxy 511

Using Excel and R to Conduct a Hypothesis Test for ρxy 511

Limitations of Correlation Analysis 513

The Linear Regression Model 515

The Simple Linear Regression Model 516

Using Excel and R to Estimate a Simple Linear Regression Model 520

The Multiple Linear Regression Model 521

Using Excel and R to Estimate a Multiple Linear Regression Model 523

Goodness-of-Fit Measures 528

The Standard Error of the Estimate 529

The Coefficient of Determination, R2 530

Synopsis of Introductory Case 534

Writing with Statistics 536

Conceptual Review 538

Additional Exercises and Case Studies 539

Case Studies 541

Appendix 14.1: Guidelines for Other Software Packages 543

CHAPTER 15

INFERENCE WITH REGRESSION MODELS 544

Tests of Significance 546

Test of Individual Significance 546

Using a Confidence Interval to Determine Individual Significance 548

A Test for a Nonzero Slope Coefficient 549

Test of Joint Significance 551

Reporting Regression Results 553

Synopsis of Introductory Case 554

A General Test of Linear Restrictions 558

Interval Estimates for the Response Variable 563

Model Assumptions and Common Violations 567

Common Violation 1: Nonlinear Patterns 569

Detection 569

Remedy 571

Common Violation 2: Multicollinearity 571

Detection 571

Remedy 572

Common Violation 3: Changing Variability 572

Detection 573

Remedy 574

Common Violation 4: Correlated Observations 574

Detection 574

Remedy 575

Common Violation 5: Excluded Variables 575

Remedy 575

Summary 576

Using Excel and R to Construct Residual Plots 576

Writing with Statistics 580

Conceptual Review 582

Additional Exercises and Case Studies 584

Exercises 584

Case Studies 586

Appendix 15.1: Guidelines for Other Software Packages 588

CHAPTER 16

REGRESSION MODELS FOR NONLINEAR RELATIONSHIPS 590

Polynomial Regression Models 592

Regression Models with Logarithms 601

A Log-Log Model 602

The Logarithmic Model 603

The Exponential Model 605

Comparing Linear and Log-Transformed Models 608

Using Excel and R to Compare Linear and Log-Transformed Models 609

Synopsis of Introductory Case 611

Writing with Statistics 614

Conceptual Review 616

Additional Exercises and Case Studies 617

Exercises 617

Case Studies 619

Appendix 16.1: Guidelines for Other Software Packages 621

CHAPTER 17

REGRESSION MODELS WITH DUMMY VARIABLES 624

Dummy Variables 626

Qualitative Explanatory Variable with Two Categories 626

Qualitative Explanatory Variable with Multiple Categories 629

Interactions with Dummy Variables 635

Synopsis of Introductory Case 639

Binary Choice Models 641

The Linear Probability Model 641

The Logit Model 643

Using R to Estimate a Logit Model 646

Writing with Statistics 649

Conceptual Review 650

Additional Exercises and Case Studies 651

Exercises 651

Case Studies 655

Appendix 17.1: Guidelines for Other Software Packages 657

PART SIX

Supplementary Topics

CHAPTER 18

TIME SERIES AND FORECASTING 658

Choosing a Forecasting Model 660

Model Selection Criteria 661

Smoothing Techniques 662

Moving Average Methods 662

Exponential Smoothing Methods 665

Using Excel and R for Moving Averages and Exponential Smoothing 667

Trend Forecasting Models 670

The Linear Trend 670

The Exponential Trend 671

Polynomial Trends 674

Trend and Seasonality 678

Decomposition Analysis 678

Extracting Seasonality 679

Extracting Trend 681

Forecasting with Decomposition Analysis 682

Seasonal Dummy Variables 683

Synopsis of Introductory Case 686

Causal Forecasting Methods 688

Lagged Regression Models 688

Using R to Estimate Lagged Regression Models 690

Writing with Statistics 692

Conceptual Review 694

Additional Exercises and Case Studies 695

Exercises 695

Case Studies 698

Appendix 18.1: Guidelines for Other Software Packages 700

CHAPTER 19

RETURNS, INDEX NUMBERS, AND INFLATION 702

Investment Return 704

Nominal versus Real Rates of Return 706

Index Numbers 708

Simple Price Indices 708

Unweighted Aggregate Price Index 710

Weighted Aggregate Price Index 711

Synopsis of Introductory Case 715

Using Price Indices to Deflate a Time Series 717

Inflation Rate 719

Writing with Statistics 722

Conceptual Review 723

Additional Exercises and Case Studies 724

Exercises 724

Case Studies 726

CHAPTER 20

NONPARAMETRIC TESTS 728

Testing a Population Median 730

The Wilcoxon Signed-Rank Test for a Population Median 730

Using a Normal Distribution Approximation for T 733

Using R to Test a Population Median 734

Testing Two Population Medians 736

The Wilcoxon Signed-Rank Test for a Matched-Pairs Sample 736

Using R to Test for Median Differences from a Matched-Pairs Sample 737

The Wilcoxon Rank-Sum Test for Independent Samples 738

Using R to Test for Median Differences from Independent Samples 740

Using a Normal Distribution Approximation for W 741

Testing Three or More Population Medians 744

The Kruskal-Wallis Test for Population Medians 744

Using R to Conduct a Kruskal-Wallis Test 746

The Spearman Rank Correlation Text 749

Using R to Test the Spearman Rank Correlation Coefficient 751

Using a Normal Distribution Approximation for rS 752

Summary of Parametric and Nonparametric Tests 752

Synopsis of Introductory Case 753

Appendix A

Appendix B

Appendix C

The Sign Test 755

Tests Based on Runs 759

The Method of Runs Above and Below the Median 760

Using R to Conduct the Runs Test 762

Writing with Statistics 764

Conceptual Review 765

Additional Exercises and Case Studies 767

Exercises 767

Case Studies 769

Appendix 20.1: Guidelines for Other Software Packages 771

APPENDIXES

Getting Started with R 774

Tables 781

Answers to Selected Even-Numbered Exercises 793

Glossary G-1

Index I-1

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