1 COLLECTION AND PRESENTATION OF DATA 1
1.1 Introduction 2
1.2 Population and Sample Data 3
1.3 Sampling and Statistical Analysis 5
1.4 Data Sources 9
1.5 Experiments and Randomization 13
1.6 Other Types of Samples 14
1.7 Organizing，Condensing and Presenting Quantitative Data 17
Frequency Distributions 17
Histograms 21
Cumulative Frequency Distributions 21
1.8 Stem-and-Leaf Graphics （Optional） 26
1.9 Presenting Qualitative Data 31
2 DESCRIPTION AND SUMMARY OF DATA 43
2.1 Introduction 44
2.2 Descriptive Summary Measures 45
2.3 The Mean as a Measure of Central Tendency 46
2.4 The Weighted Mean 49
Approximation Method 49
Comments on Approximating a Mean 51
Exact Method 52
2.5 Applications of the Mean to Quality Control 53
2.6 The Median as a Measure of Central Tendency 57
Locating the Median in the Original Data Set 57
Locating the Median in Grouped Data 60
Algebraic Approximation of the Median 60
Graphical Approximation of the Median 61
2.7 The Mode as a Measure of Central Tendency 64
2.8 Percentiles，Deciles，and Quartiles 66
2.9 Skewness 68
2.10 Measures of Dispersion 68
2.11 The Range 72
2.12 The Interquartile Range and the Box Plot 75
2.13 Variance and Standard Deviations 77
2.14 The Variance and Standard Deviation in Frequency Form 82
2.15 Data Location and the Standard Deviation 86
2.16 Looking Ahead 89
3 PROBABILITY 105
3.1 Introduction 106
3.2 Relative Frequency and Probability 107
3.3 Experiments，Outcomes，and Probability 107
3.4 Events and Probability 110
3.5 Determining the Sample Space 111
3.6 Counting Techniques 113
3.7 Multiple Events 118
Unions and Intersections 119
Complements 119
Conditional Probability 121
3.8 Independence 123
3.9 Subjective Versus Objective Probability 133
3.10 Concluding Comments 137
4 RANDOM VARIABLES 143
4.1 Introduction 144
4.2 Random Variables and Probability 145
4.3 Probability Mass 147
4.4 The Expected Value of a Random Variable 148
4.5 The Dispersion of a Random Variable 152
4.6 Risk Assessment 154
Standard Deviation Comparison 154
Coefficient of Variation Comparison 155
4.7 Multiple Random Variables 158
4.8 Joint Probability Distributions 158
4.9 Additive Probability 163
4.10 Linear Functions of Random Variables 165
4.11 Expected Value and Variance of Sums of Random Variables 166
4.12 Covariance and Dependent Random Variables （Optional） 169
4.13 Concluding Comments 172
5 DISTRIBUTIONS OF DISCRETE RANDOM VARIABLES 179
5.1 Introduction 180
5.2 The Binomial Distribution 181
5.3 The Binomial Probability Mass Function 183
Determined with a Computer 185
Determined with a Binomial Table 186
5.4 Location and Dispersion 193
5.5 The Hypergeometric Distribution 200
5.6 The Poisson Distribution 204
5.7 Concluding Comments 211
6 DISTRIBUTIONS OF CONTINUOUS RANDOM VARIABLES 217
6.1 Introduction 218
6.2 Continuous Random Variables and Probability Distributions 219
6.3 Normal Distributions 226
6.4 The Standard Normal Distribution 228
6.5 Calculations with the Standard Normal Table 233
6.6 The Lognormal Distribution （Optional） 240
6.7 Concluding Comments 245
7 SAMPLING AND SAMPLING DISTRIBUTIONS 251
7.1 Introduction 252
7.2 Probability Samples 253
7.3 Simple Random Samples 253
Blind Draw 254
Random Number Table 255
Computerized Random Number Generator 256
7.4 Systematic Sampling 257
7.5 Stratified Sampling 259
7.6 Cluster Sampling 260
7.7 Sampling Distribution of the Sum of Random Variables 261
7.8 Sampling Distribution of the Sample Mean 265
7.9 Sampling Distribution of the Sample Mean for Large Samples 274
7.10 Sampling Distribution of the Sample Mean for Small Samples 278
7.11 Sampling Distribution of the Sample Proportion 281
7.12 Concluding Comments 284
Appendix 7 Avoiding Errors in Sampling 289
Validity 289
Reliability 290
Measurement 291
Omitted and Missing Observations 291
8 ESTIMATION 295
8.1 Introduction 296
8.2 Point Estimation 297
8.3 Properties of Estimators 298
8.4 Confidence Intervals 301
8.5 Confidence Interval for the Population Mean 302
8.6 Level of Confidence 305
8.7 When σ Is Unknown 307
8.8 Confidence Interval for the Mean，σ Unknown （and n small） 310
8.9 Estimating the Population Proportion π 315
8.10 Selecting the Sample Size 318
Selecting a Sample Size to Estimate μ 318
Selecting a Sample Size to Estimate π 320
8.11 Estimating the Population Median by Iteration （Optional） 322
8.12 Estimating the Population Median by the Bootstrap （Optional） 324
8.13 Concluding Comments 326
9 SINGLE SAMPLE HYPOTHESIS TESTING 335
9.1 Introduction 336
9.2 Hypotheses：An Illustration 337
Types and Cost of Errors 337
Stating the Hypotheses 339
9.3 Decision Rule：An Illustration 340
p-Value 340
Decision Rule 341
9.4 General Procedures for Hypothesis Testing 345
9.5 The Null and Alternative Hypotheses （Step 1） 345
One-Tailed Tests 347
Two-Tailed Tests 348
9.6 The Probabilities of Type I and Ⅱ Errors （Step 2） 349
One-Tailed Hypothesis Tests 351
Two-Tailed Hypothesis Tests 351
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 Test 359
Determining a p-Value for a Two-Tailed Test 362
9.10 Reaching a Conclusion （Step 6） 363
Using Confidence Intervals in Conclusions 364
Maintaining Uncertainty in Conclusions 364
9.11 Testing a Population Proportion 369
9.12 Test of the Median （Optional） 372
9.13 Bayesian Hypothesis Testing （Optional） 374
9.14 Concluding Comments 375
Appendix 9A The Type I and Type Ⅱ Error Tradeoff and the Effect of Sample Size 386
Appendix 9B The Operating-Characteristic Curve and the Power of a Test 389
Appendix 9C The Operating-Characteristic Curve and Acceptance Sampling 394
Appendix 9D Type I and Type Ⅱ Errors and Sample Size Selection 396
10 TWO-SAMPLE HYPOTHESIS TESTING 399
10.1 Introduction 400
10.2 Difference Between Means 401
When Variances Are Known （or Samples are Large） 402
When Variances Are Unknown but Assumed Equal 405
10.3 Test of Equality of Variances 410
One-Tailed Test 411
Two-Tailed Test 414
10.4 Small Samples of Different Size and Different Variances 417
10.5 Two-Sample Test without the Assumption of Normality 418
10.6 Matched Pairs 424
10.7 Testing Matched Pairs without the Assumption of Normality 430
10.8 Testing the Difference between Population Proportions 432
10.9 The Median Test for Two Samples （Optional） 436
10.10 Concluding Comments 438
11 ANALYSIS OF VARIANCE AND CONTINGENCY TABLES 447
11.1 Introduction 448
11.2 Variability Between and within Samples 448
Variability Between Samples 452
Variability within Samples 453
11.3 Comparing Critical and Calculated Values 454
11.4 The Analysis of Variance （ANOVA） Table 457
11.5 Two-Way ANOVA 464
11.6 Testing in Multiple Factor ANOVA 467
11.7 Multiple Factor ANOVA with a Computer 468
11.8 The Chi-Square Test for Independence 472
The Chi-Square Statistic 472
The p-value 475
11.9 Critical Values and the Chi-Square Distribution 475
11.10 Nonparametric ANOVA （Optional） 479
11.11 Looking Ahead 483
12 CORRELATION AND REGRESSION ANALYSIS WITHIN A SAMPLE 493
12.1 Introduction 494
12.2 Speed and Death：An Illustration 494
12.3 Conditional Means and Deviations 495
12.4 Deviations from the Means 498
12.5 Measures of Covariance 502
12.6 Correlation 504
12.7 The Regression Line 513
12.8 Errors in Predictions 516
12.9 The Method of Least Squares 517
12.10 Goodness-of-Fit and Correlation 524
12.11 Rank Correlation Measures （Optional） 530
12.12 Linear Regression and Correlation Via Computers 532
13 THE TWO-VARIABLE POPULATION MODEL 549
13.1 Introduction 550
13.2 The Phillips Curve 550
13.3 Deterministic Versus Stochastic Relationships 551
13.4 Estimation of Coefficients 555
13.5 The Confidence Interval for the Expected Value of y 559
13.6 The Prediction Interval for an Individual Value ofy 563
13.7 The Sampling Distribution of b 565
13.8 Testing Hypotheses About Individual Coefficients 567
13.9 Two-Tailed Test 568
13.10 Two-Tailed Test and Computer Output 570
13.11 Two-Tailed Test and Confidence Intervals 572
13.12 One-Tailed Test 575
13.13 Tests of Correlation （Optional） 578
13.14 Violations of the Assumptions 579
Normality 579
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 Comments 601
14 MULTIPLE REGRESSION 615
14.1 Introduction 616
14.2 The Case of Equal Pay 616
14.3 Interpretation of Coefficients and the Prediction of y 618
14.4 Least Squares in Multiple Regression 623
14.5 Assumptions，Estimation，and Hypotheses Testing 626
14.6 Estimation of a Conditional Expected Value of y 633
14.7 Prediction of an Individual Value ofy 635
14.8 Hypotheses Testing 636
14.9 Confidence Interval for βj 642
14.10 Multiple Coefficient of Determination 644
14.11 Adjusted Coefficient of Determination 647
14.12 Testing the Population Model 648
14.13 Problems in Estimation 651
Insufficient Variability within an Explanatory Variable 651
Linear Relationship Among Explanatory Variables：Multicollinearity 652
14.14 Stepwise Regression （Optional） 656
14.15 Concluding Comments 662
15 TIME SERIES ANALYSIS AND FORECASTING 677
15.1 Introduction 678
15.2 Time Series Components 678
15.3 Trend Analysis 682
Forecasting with a Trend Line 682
Detrended Time Series 683
15.4 Seasonal Variation 686
15.5 Residual Analysis 695
15.6 Durbin-Watson Test 696
15.7 Runs Test 699
15.8 Dynamic Model 703
Building a Dynamic Model 703
Forecasting with a Dynamic Model 705
15.9 Testing for Autocorrelated Errors in Dynamic Models 707
15.10 Models Involving First Differences 708
15.11 Causal Model Building for Forecasting 712
15.12 Tradeoffs in Modeling 719
15.13 Concluding Comments 724
16 INDEX NUMBERS 739
16.1 Introduction 740
16.2 Measuring Price Change 740
16.3 Index Numbers 741
16.4 Other Index Weighting Schemes （Optional） 745
16.5 Chaining of Index Numbers 747
16.6 Splicing of Index Numbers 749
16.7 Seasonality and Smoothing of Index Numbers 754
Comparable Period Differencing 754
Moving Averages 754
Concluding Comments 760
17 DECISION ANALYSIS 767
17.1 Introduction 768
17.2 Decision Trees 768
17.3 Risk in Decision Making 772
17.4 Expected Utility Theory 772
17.5 An Application of Expected Utility to Production 775
17.6 Decision Analysis and New Sample Information 780
17.7 Computing Probabilities with Bayes’ Rule 784
17.8 Computing Probabilities with a Computer Spreadsheet 787
17.9 Optimal Decisions Based on Posterior Probabilities 788
17.10A Computer Based Decision-Making System 793
17.11 An Application of Expected Utility to the Value of Life （Optional） 796
17.12 Empirical Observations on Expected Utility Theory 799
18 STATISTICAL QUALITY CONTROL AND QUALITY MANAGEMENT 807
18.1 Introduction 808
18.2 A Perspective on Production and Quality Control 809
18.3 Statistical Quality Control and Graphical Tools 811
Flowcharts 812
Pareto Chart 814
Fishbone Diagram 816
Histogram 817
18.4 Statistical Process Control 817
18.5 Statistical Process Control：A Control Chart 818
18.6 Statistical Process Control：Examining Process Variability 823
18.7 Proportions and Their Application to Process Control 826
The c Chart 830
18.8 Acceptance Sampling by Attributes 833
18.9 Concluding Comments 835
Appendices 843
Short Answers to Selected Even-Numbered Exercises 901
Index 929