《STATISTICS%FOR BUSINESS AND ECONOMICS》

1 COLLECTION AND PRESENTATION OF DATA1

1.1 Introduction2

1.2 Population and Sample Data3

1.3 Sampling and Statistical Analysis5

1.4 Data Sources9

1.5 Experiments and Randomization13

1.6 Other Types of Samples14

1.7 Organizing，Condensing and Presenting Quantitative Data17

Frequency Distributions17

Histograms21

Cumulative Frequency Distributions21

1.8 Stem-and-Leaf Graphics （Optional）26

1.9 Presenting Qualitative Data31

2 DESCRIPTION AND SUMMARY OF DATA43

2.1 Introduction44

2.2 Descriptive Summary Measures45

2.3 The Mean as a Measure of Central Tendency46

2.4 The Weighted Mean49

Approximation Method49

Comments on Approximating a Mean51

Exact Method52

2.5 Applications of the Mean to Quality Control53

2.6 The Median as a Measure of Central Tendency57

Locating the Median in the Original Data Set57

Locating the Median in Grouped Data60

Algebraic Approximation of the Median60

Graphical Approximation of the Median61

2.7 The Mode as a Measure of Central Tendency64

2.8 Percentiles，Deciles，and Quartiles66

2.9 Skewness68

2.10 Measures of Dispersion68

2.11 The Range72

2.12 The Interquartile Range and the Box Plot75

2.13 Variance and Standard Deviations77

2.14 The Variance and Standard Deviation in Frequency Form82

2.15 Data Location and the Standard Deviation86

2.16 Looking Ahead89

3 PROBABILITY105

3.1 Introduction106

3.2 Relative Frequency and Probability107

3.3 Experiments，Outcomes，and Probability107

3.4 Events and Probability110

3.5 Determining the Sample Space111

3.6 Counting Techniques113

3.7 Multiple Events118

Unions and Intersections119

Complements119

Conditional Probability121

3.8 Independence123

3.9 Subjective Versus Objective Probability133

3.10 Concluding Comments137

4 RANDOM VARIABLES143

4.1 Introduction144

4.2 Random Variables and Probability145

4.3 Probability Mass147

4.4 The Expected Value of a Random Variable148

4.5 The Dispersion of a Random Variable152

4.6 Risk Assessment154

Standard Deviation Comparison154

Coefficient of Variation Comparison155

4.7 Multiple Random Variables158

4.8 Joint Probability Distributions158

4.9 Additive Probability163

4.10 Linear Functions of Random Variables165

4.11 Expected Value and Variance of Sums of Random Variables166

4.12 Covariance and Dependent Random Variables （Optional）169

4.13 Concluding Comments172

5 DISTRIBUTIONS OF DISCRETE RANDOM VARIABLES179

5.1 Introduction180

5.2 The Binomial Distribution181

5.3 The Binomial Probability Mass Function183

Determined with a Computer185

Determined with a Binomial Table186

5.4 Location and Dispersion193

5.5 The Hypergeometric Distribution200

5.6 The Poisson Distribution204

5.7 Concluding Comments211

6 DISTRIBUTIONS OF CONTINUOUS RANDOM VARIABLES217

6.1 Introduction218

6.2 Continuous Random Variables and Probability Distributions219

6.3 Normal Distributions226

6.4 The Standard Normal Distribution228

6.5 Calculations with the Standard Normal Table233

6.6 The Lognormal Distribution （Optional）240

6.7 Concluding Comments245

7 SAMPLING AND SAMPLING DISTRIBUTIONS251

7.1 Introduction252

7.2 Probability Samples253

7.3 Simple Random Samples253

Blind Draw254

Random Number Table255

Computerized Random Number Generator256

7.4 Systematic Sampling257

7.5 Stratified Sampling259

7.6 Cluster Sampling260

7.7 Sampling Distribution of the Sum of Random Variables261

7.8 Sampling Distribution of the Sample Mean265

7.9 Sampling Distribution of the Sample Mean for Large Samples274

7.10 Sampling Distribution of the Sample Mean for Small Samples278

7.11 Sampling Distribution of the Sample Proportion281

7.12 Concluding Comments284

Appendix 7 Avoiding Errors in Sampling289

Validity289

Reliability290

Measurement291

Omitted and Missing Observations291

8 ESTIMATION295

8.1 Introduction296

8.2 Point Estimation297

8.3 Properties of Estimators298

8.4 Confidence Intervals301

8.5 Confidence Interval for the Population Mean302

8.6 Level of Confidence305

8.7 When σ Is Unknown307

8.8 Confidence Interval for the Mean，σ Unknown （and n small）310

8.9 Estimating the Population Proportion π315

8.10 Selecting the Sample Size318

Selecting a Sample Size to Estimate μ318

Selecting a Sample Size to Estimate π320

8.11 Estimating the Population Median by Iteration （Optional）322

8.12 Estimating the Population Median by the Bootstrap （Optional）324

8.13 Concluding Comments326

9 SINGLE SAMPLE HYPOTHESIS TESTING335

9.1 Introduction336

9.2 Hypotheses：An Illustration337

Types and Cost of Errors337

Stating the Hypotheses339

9.3 Decision Rule：An Illustration340

p-Value340

Decision Rule341

9.4 General Procedures for Hypothesis Testing345

9.5 The Null and Alternative Hypotheses （Step 1）345

One-Tailed Tests347

Two-Tailed Tests348

9.6 The Probabilities of Type I and Ⅱ Errors （Step 2）349

One-Tailed Hypothesis Tests351

Two-Tailed Hypothesis Tests351

9.7 Selecting a Test Statistic （Step 3）356

9.8 The Sample （Step 4）358

9.9 Determining p-Values （Step 5）358

Determining the p-Value for a One-Tailed t Test359

Determining a p-Value for a Two-Tailed Test362

9.10 Reaching a Conclusion （Step 6）363

Using Confidence Intervals in Conclusions364

Maintaining Uncertainty in Conclusions364

9.11 Testing a Population Proportion369

9.12 Test of the Median （Optional）372

9.13 Bayesian Hypothesis Testing （Optional）374

9.14 Concluding Comments375

Appendix 9A The Type I and Type Ⅱ Error Tradeoff and the Effect of Sample Size386

Appendix 9B The Operating-Characteristic Curve and the Power of a Test389

Appendix 9C The Operating-Characteristic Curve and Acceptance Sampling394

Appendix 9D Type I and Type Ⅱ Errors and Sample Size Selection396

10 TWO-SAMPLE HYPOTHESIS TESTING399

10.1 Introduction400

10.2 Difference Between Means401

When Variances Are Known （or Samples are Large）402

When Variances Are Unknown but Assumed Equal405

10.3 Test of Equality of Variances410

One-Tailed Test411

Two-Tailed Test414

10.4 Small Samples of Different Size and Different Variances417

10.5 Two-Sample Test without the Assumption of Normality418

10.6 Matched Pairs424

10.7 Testing Matched Pairs without the Assumption of Normality430

10.8 Testing the Difference between Population Proportions432

10.9 The Median Test for Two Samples （Optional）436

10.10 Concluding Comments438

11 ANALYSIS OF VARIANCE AND CONTINGENCY TABLES447

11.1 Introduction448

11.2 Variability Between and within Samples448

Variability Between Samples452

Variability within Samples453

11.3 Comparing Critical and Calculated Values454

11.4 The Analysis of Variance （ANOVA） Table457

11.5 Two-Way ANOVA464

11.6 Testing in Multiple Factor ANOVA467

11.7 Multiple Factor ANOVA with a Computer468

11.8 The Chi-Square Test for Independence472

The Chi-Square Statistic472

The p-value475

11.9 Critical Values and the Chi-Square Distribution475

11.10 Nonparametric ANOVA （Optional）479

11.11 Looking Ahead483

12 CORRELATION AND REGRESSION ANALYSIS WITHIN A SAMPLE493

12.1 Introduction494

12.2 Speed and Death：An Illustration494

12.3 Conditional Means and Deviations495

12.4 Deviations from the Means498

12.5 Measures of Covariance502

12.6 Correlation504

12.7 The Regression Line513

12.8 Errors in Predictions516

12.9 The Method of Least Squares517

12.10 Goodness-of-Fit and Correlation524

12.11 Rank Correlation Measures （Optional）530

12.12 Linear Regression and Correlation Via Computers532

13THE TWO-VARIABLE POPULATION MODEL549

13.1 Introduction550

13.2 The Phillips Curve550

13.3 Deterministic Versus Stochastic Relationships551

13.4 Estimation of Coefficients555

13.5 The Confidence Interval for the Expected Value of y559

13.6 The Prediction Interval for an Individual Value ofy563

13.7 The Sampling Distribution of b565

13.8 Testing Hypotheses About Individual Coefficients567

13.9 Two-Tailed Test568

13.10 Two-Tailed Test and Computer Output570

13.11 Two-Tailed Test and Confidence Intervals572

13.12 One-Tailed Test575

13.13 Tests of Correlation （Optional）578

13.14 Violations of the Assumptions579

Normality579

Lack of Linearity in a Hyperbolic Scatterplot （Optional）581

Lack of Linearity in Scatterplots with Multiplicative Growth （Optional）583

Some Other Data Transformations （Optional）586

Nonconstant Error Term Variability （Optional）594

Regressor Error Term Correlation （Optional）595

13.15 Concluding Comments601

14MULTIPLE REGRESSION615

14.1 Introduction616

14.2 The Case of Equal Pay616

14.3 Interpretation of Coefficients and the Prediction of y618

14.4 Least Squares in Multiple Regression623

14.5 Assumptions，Estimation，and Hypotheses Testing626

14.6 Estimation of a Conditional Expected Value of y633

14.7 Prediction of an Individual Value ofy635

14.8 Hypotheses Testing636

14.9 Confidence Interval for βj642

14.10 Multiple Coefficient of Determination644

14.11 Adjusted Coefficient of Determination647

14.12 Testing the Population Model648

14.13 Problems in Estimation651

Insufficient Variability within an Explanatory Variable651

Linear Relationship Among Explanatory Variables：Multicollinearity652

14.14 Stepwise Regression （Optional）656

14.15 Concluding Comments662

15TIME SERIES ANALYSIS AND FORECASTING677

15.1 Introduction678

15.2 Time Series Components678

15.3 Trend Analysis682

Forecasting with a Trend Line682

Detrended Time Series683

15.4 Seasonal Variation686

15.5 Residual Analysis695

15.6 Durbin-Watson Test696

15.7 Runs Test699

15.8 Dynamic Model703

Building a Dynamic Model703

Forecasting with a Dynamic Model705

15.9 Testing for Autocorrelated Errors in Dynamic Models707

15.10 Models Involving First Differences708

15.11 Causal Model Building for Forecasting712

15.12 Tradeoffs in Modeling719

15.13 Concluding Comments724

16 INDEX NUMBERS739

16.1 Introduction740

16.2 Measuring Price Change740

16.3 Index Numbers741

16.4 Other Index Weighting Schemes （Optional）745

16.5 Chaining of Index Numbers747

16.6 Splicing of Index Numbers749

16.7 Seasonality and Smoothing of Index Numbers754

Comparable Period Differencing754

Moving Averages754

Concluding Comments760

17 DECISION ANALYSIS767

17.1 Introduction768

17.2 Decision Trees768

17.3 Risk in Decision Making772

17.4 Expected Utility Theory772

17.5 An Application of Expected Utility to Production775

17.6 Decision Analysis and New Sample Information780

17.7 Computing Probabilities with Bayes’ Rule784

17.8 Computing Probabilities with a Computer Spreadsheet787

17.9 Optimal Decisions Based on Posterior Probabilities788

17.10A Computer Based Decision-Making System793

17.11 An Application of Expected Utility to the Value of Life （Optional）796

17.12 Empirical Observations on Expected Utility Theory799

18 STATISTICAL QUALITY CONTROL AND QUALITY MANAGEMENT807

18.1 Introduction808

18.2 A Perspective on Production and Quality Control809

18.3 Statistical Quality Control and Graphical Tools811

Flowcharts812

Pareto Chart814

Fishbone Diagram816

Histogram817

18.4 Statistical Process Control817

18.5 Statistical Process Control：A Control Chart818

18.6 Statistical Process Control：Examining Process Variability823

18.7 Proportions and Their Application to Process Control826

The c Chart830

18.8 Acceptance Sampling by Attributes833

18.9 Concluding Comments835

Appendices843

Short Answers to Selected Even-Numbered Exercises901

Index929