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fourth edition
Ronald M. WeiersEberly College of Business andInformation TechnologyIndiana University of Pennsylvania
DUXBURY
THOMSON LEARNING
Australia • Canada * Mexico • SingaporeSpain • United Kingdom • United States
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A Preview of Business Statistics 1
Visual Descriptions of Data 17
Statistical Descriptions of Data 71
Data Collection and Sampling Methods
Probability: Review of Basic Concepts119
157
197239
Discrete Probability Distributions
Continuous Probability Distributions
Sampling Distributions 281
Estimation from Sample Data 307
Hypothesis Tests Involving a Sample Mean
or Proportion 351
Hypothesis Tests Involving Two Sample Means
or Proportions 407
Analysis of Variance Tests 457
Chi-Square Applications 517
Nonparametric Methods 563
Simple Linear Regression and Correlation 609
Multiple Regression and Correlation 659
Model Building 707
Models for Time Series and Forecasting 751
Decision Theory 811
Total Quality Management 839
BRIEF CONTENTS
\ \ j/ u /V
PART ONE
Business Statistics: Introduction and BackgroundA Preview of Business Statistics
1 1.1 Introduction 2Timely Topic, Tattered Image 2
What Is Business Statistics? 2
For the Consumer as Well as the Practitioner 3
PRACTITIONER PERSPECTIVE:
Describing Tourism at Niagara Falls 3
1.2 Statistics: Yesterday and Today 4Yesterday 4
Today 5
1.3 Descriptive versus Inferential StatisticsDescriptive Statistics 6
Inferential Statistics 6
1.4 Types of Variables and Scales of MeasurementQualitative Variables 9
Quantitative Variables 9
Scales of Measurement 10
1.5 Statistics in Business Decisions 12
1.6 Business Statistics: Tools versus Tricks
STATISTICS IN ACTION 1.1:
High Stakes on the Interstate: Car Phones and Accidents 14
1.7 Summary 14
13
CONTENTS Vll
Visual Description of Data 17
2.1 Introduction 18
2.2 The Data Array and the Frequency Distribution 18The Data Array 20
PRACTITIONER PERSPECTIVE:
Scoring Visual Points with InFocus 20
The Frequency Distribution 22
2.3 The Stem-and-Leaf Display and the Dotplot 29The Stem-and-Leaf Display 30
The Dotplot 32
2.4 Visual Representation of the Data 34Popular Graphical Methods 34
The Abuse of Visual Displays 44
STATISTICS IN ACTION 2.1 :
These Words Are Better Than a Ninth of a Picture 46
2.5 The Scatter Diagram 48
2.6 Tabulation, Contingency Tables,and the Excel PivotTable Wizard 54Simple Tabulation 54
Cross-Tabulation (Contingency Table) 54
2.7 Summary 60
Statistical Description of Data 71
3.1 Introduction 72
PRACTITIONER PERSPECTIVE:
Statistical Descriptors and the Bureau of the Census 73
3.2 Statistical Description: Measures of Central Tendency 74The Arithmetic Mean 74
The Weighted Mean 76
The Median 76
STATISTICS IN ACTION 3.1:
The United States, a People of Means 77
The Mode 78
Distribution Shape and Measures of Central Tendency 78
STATISTICS IN ACTION 3.2:
U.S. Males Post Skewed Incomes -80
3.3 Statistical Description: Measures of Dispersion 83Range 84
Quantiles 86
viii CONTENTS
Mean Absolute Deviation (MAD) 87
Variance and Standard Deviation 88
3.4 Additional Dispersion Topics 93The Box-and-Whisker Plot 93
Chebyshev's Theorem 95
The Empirical Rule 96
Standardized Data 96
The Coefficient of Variation 99
3.5 Descriptive Statistics from Grouped Data 101Arithmetic Mean from Grouped Data 102
Variance and Standard Deviation from Grouped Data 103
3.6 Statistical Measures of Association 104A Closing Note 107
STATISTICS IN ACTION 3.3:
The Consumer Price Index 108
3.7 Summary 109
Data Collection and Sampling Methods 119
4.1 Introduction 120
4.2 Research Basics 121Types of Studies 121
PRACTITIONER PERSPECTIVE:Data Collection with The Archimedes Group 122
The Research Process 123
Primary versus Secondary Data 123
4.3 Survey Research 124Types of Surveys 124
Questionnaire Design 124
Sampling Considerations in Survey Research 126
Errors in Survey Research 127
4.4 Experimentation and Observational Research 128Experimentation 128
Observational Research 130
4.5 Secondary Data 131Internal Sources 131
External Sources 132
Data Warehousing and Data Mining 133
Internet Data Sources 134
Evaluating Secondary Data 135
STATISTICS IN ACTION 4 .1 :
The Optimistic Homebuilders 136
CONTENTS ix
4.6 The Basics of Sampling 137Selected Terms 137
Why a Sample Instead of a Census? 137
4.7 Sampling Methods 139Probability Sampling 139
Nonprobability Sampling 146
STATISTICS IN ACTION 4.2:
Shopping for Jurors 147
STATISTICS IN ACTION 4.3:
A Sample of Sampling by Giving Away Samples 148
4.8 Summary 149
PART TWO
ProbabilityProbability; Review of Basic Concepts
158
157
5.1 Introduction
PRACTITIONER PERSPECTIVE:
Probabilities and Insurance with Good and Associates 159
5.2 Probability: Terms and ApproachesBasic Terms 160
The Classical Approach 161
The Relative Frequency Approach 161
The Subjective Approach 162
STATISTICS IN ACTION 5.1 :Relative Frequencies and Travel Safety 163
Probabilities and "Odds" 164
160
165
169
172
5.3 Unions and Intersections of Events
5.4 Addition Rules for ProbabilityWhen Events Are Mutually Exclusive 169
When Events Are Not Mutually Exclusive 170
5.5 Multiplication Rules for ProbabilityWhen Events Are Independent 173
When Events Are Not Independent 173
5.6 Bayes' Theorem and the Revision of Probabilities
5.7 Counting: Permutations and Combinations 183Fundamentals of Counting 183
STATISTICS IN ACTION 5.2:
Computer Assistance in the Name Game 184
177
CONTENTS
Permutations 185
Combinations 186
5.8 Summary 187
Discrete Probability Distributions 197
6.1 Introduction 198Random Variables: Discrete versus Continuous 199
PRACTITIONER PERSPECTIVE:
Saving Lives and Examining Data with Citizens' Ambulance 199
The Nature of a Discrete Probability Distribution 200
The Mean and Variance of a Discrete Probability Distribution 203
STATISTICS IN ACTION 6.1:
The Discrete Distribution That Took a Day Off 205
6.2 The Binomial Distribution 207Description and Applications 207
Using the Binomial Tables 211
Additional Comments on the Binomial Distribution 215
6.3 The Poisson Distribution 219Description and Applications 219
STATISTICS IN ACTION 6.2:Football Injuries and the Poisson Distribution 220
Using the Poisson Tables 222
The Poisson Approximation to the Binomial Distribution 225
6.4 Simulating Observations from aDiscrete Probability Distribution 227
6.5 Summary 231
Continuous Probability Distributions : 239
7.1 Introduction 240
PRACTITIONER PERSPECTIVE:
Navigating Normal Curves with Thorndike Sports Equipment 241
7.2 The Normal Distribution 242Description and Applications 242
Areas Beneath the Normal Curve 243
7.3 The Standard Normal Distribution 246Description and Applications 246
Using the Standard Normal Distribution Table 247
STATISTICS IN ACTION 7.1:
SAT Math Scores and the Normal Distribution 248
CONTENTS xi
7.4 The Normal Approximation tothe Binomial Distribution 258The Binomial Distribution: A Brief Review 258
The Mean and Standard Deviation 259
Correction for Continuity 259
The Approximation Procedure 260
7.5 The Exponential Distribution 264Description and Applications 264
Examples 265
7.6 Simulating Observations from aContinuous Probability Distribution 270
7.7 Summary 272
PART THREE
Sampling Distributions and EstimationSampling Distributions 281
8 8.1
8.2
8.3
8.4
8.5
8.6
8.7
Introduction 282
A Preview of Sampling Distributions
The Sampling Distribution of the MeanWhen the Population Is Normally Distributed 285
When the Populations Is Not Normally Distributed 288
283
285
The Sampling Distribution of the Proportion 291
Sampling Distributions When the Population Is Finite 294
Computer Simulation of Sampling Distributions 296
Summary 300
Estimation from Sample DataIntroduction
307.9 9.1 Introduction 308
PRACTITIONER PERSPECTIVE:
Estimation Relies on Sound Sampling Frame at Survey Sampling, Inc. 309
9.2 Point Estimates 310
9.3 A Preview of Interval Estimates 311
9.4 Confidence Interval Estimates for the Mean: a Known
9.5 Confidence Interval Estimates for the Mean: a- UnknownThe Student's t Distribution 319Confidence Intervals Using the f Distribution 322
314
319
xn CONTENTS
9.6 Confidence Interval Estimatesfor the Population Proportion 327
9.7 Sample Size Determination 331Estimating the Population Mean 332
Estimating the Population Proportion 333
STATISTICS IN ACTION 9.1:
Sampling Error in Survey Research 336
9.8 When the Population Is Finite 338Confidence-Interval Estimation 338
Sample Size Determination 339
9.9 Summary 342
PART FOUR
Hypothesis TestingHypothesis Tests Involving a Sample Mean or Proportion 351
.10 10.1 Introduction 352Null and Alternative Hypotheses 353
PRACTITIONER PERSPECTIVE:
Products Are Tested Extensively Before Receiving the Underwriters Laboratories Mark 353
Directional and Nondirectional Testing 354
Hypothesis Testing and the Nature of the Test 354
Errors in Hypothesis Testing 356
10.2 Hypothesis Testing: Basic Procedures 358
10.3 Testing a Mean, PopulationStandard Deviation Known 361Two-Tail Testing of a Mean, a Known 361
One-Tail Testing of a Mean, a Known 363
The p-value Approach to Hypothesis Testing 365
Computer-Assisted Hypothesis Tests and p-values 367
10.4 Confidence Intervals and Hypothesis Testing 371
10.5 Testing a Mean, PopulationStandard Deviation Unknown 372Two-Tail Testing of a Mean, a Unknown 373
One-Tail Testing of a Mean, cr Unknown 374
10.6 Testing a Proportion 381Two-Tail Testing of a Proportion 382
One-Tail Testing of a Proportion 383
CONTENTS xm
10.7 The Power of a Hypothesis Test 389Hypothesis Testing Errors and the Power of a Test 389
The Power of a Test: An Example 390
The Power Curve for a Hypothesis Test 391
The Effect of Increased Sample Size on Type I and Type II Errors 394
10.8 Summary 398
Hypothesis Tests Involving Two Sample Means or Proportions 407
11.1 Introduction 408.11PRACTITIONER PERSPECTIVE:
Comparing Sample Means and Proportions at Eddie Bauer 409
11.2 The Pooled-Variances t-Test for Comparingthe Means of Two Independent Samples 411
11.3 The Unequal-Variances t-Test for Comparingthe Means of Two Independent Samples 418
11.4 The z-Test for Comparing the Meansof Two Independent Samples 424
11.5 Comparing Two Means Whenthe Samples Are Dependent 429
11.6 Comparing Two Sample Proportions 435
STATISTICS IN ACTION 11.1:Looking for Mechanical Predators 438
11.7 Comparing the Variances ofTwo Independent Samples 442
11.8 Summary 447
Analysis of Variance Tests 457
12.1 Introduction 458.1212.2 Analysis of Variance: Basic Concepts 458
Analysis of Variance and Experimentation 458
PRACTITIONER PERSPECTIVE:
Main and Interaction Effects Are Important at Intel 459
Variation Between and Within the Groups 461
12.3 One-Way Analysis of Variance 463Purpose 463 '
Model and Assumptions 463
Procedure 464
Treatment Sum of Squares, SSTR 468
Error Sum of Squares, SSE 468
xiv CONTENTS
Total Sum of Squares, SST 4G8
Treatment Mean Square (MSTR) and Error Mean Square (MSE) 469
The Test Statistic, F 469
The Critical Value of Fand the Decision 469
Computer Outputs and Interpretation 471
One-Way ANOVA and the Pooled-Variances f-Test 473
12.4 The Randomized Block Design 479Purpose 479
Model and Assumptions 480
Procedure 481
Treatment Sum of Squares, SSTR 484
Block Sum of Squares, SSB 484
Total Sum of Squares, SST 485
Error Sum of Squares, SSE 485
Treatment Mean Square {MSTR) and Error Mean Square (MSE) 485
The Test Statistic, F 485
The Critical Value of Fand the Decision 486
Testing the Effectiveness of the Blocking Variable 487
Computer Outputs and Interpretation 488
Randomized Block ANOVA and the Dependent-Samples t-Test 488
12.5 Two-Way Analysis of Variance 493Purpose 493
Model and Assumptions 493
Procedure 495
Factor A Sum of Squares, SSA 498
Factor B Sum of Squares, SSB 499
Error Sum of Squares, SSE 500
Total Sum of Squares, SS7"5O0
Interaction Sum of Squares, SSAB 500
The Mean Square Terms 501
Computer Outputs and Interpretation 503
12.6 Summary 509
Chi-Square Applications 517
.13 13.1 Introduction 518
13.2 Basic Concepts in Chi-Square Testing 518The Chi-Square Distribution 518
PRACTITIONER PERSPECTIVE:
Using Chi-Square Tests at Walker Information 519
An Overview of the Chi-Square Tests 520
13.3 Tests for Goodness of Fit and Normality 523Purpose 523
Procedure 523
CONTENTS xv
13.4 Testing the Independence of Two Variables 534Purpose 534
Procedure 534
STATISTICS IN ACTION 13.1:
Network Popularity Comparison 538
13.5 Comparing Proportions from k Independent Samples 541Purpose 541
Procedure 542
13.6 Estimation and Tests Regardingthe Population Variance 546The Confidence Interval for a Population Variance 546
Hypothesis Tests for the Population Variance 549
13.7 Summary 552
Nonparametric Methods 563
.14 14.1 Introduction 564Nonparametric Testing 564
Advantages and Disadvantages of Nonparametric Testing 565
14.2 Wilcoxon Signed Rank Test for One Sample 566Description and Applications 566
The Normal Approximation 569
14.3 Wilcoxon Signed Rank Test forComparing Paired Samples 571Description and Applications 571
14.4 Wilcoxon Rank Rum Test forComparing Two Independent Samples 575Description and Applications 575
The Normal Approximation 577
14.5 Kruskal-Wallis Test for ComparingMore Than Two Independent Samples 579Description and Applications 579
14.6 Friedman Test for the Randomized Block Design 583Description and Applications 583
14.7 Other Nonparametric Methods 588Sign Test for Comparing Paired Samples 588
The Runs Test for Randomness 593
Lilliefors Test for Normality 595
14.8 Summary 601
xvi CONTENTS
PART FIVE
Regression, Model Building, and Time SeriesSimple Linear Regression and Correlation
Introduction
609
.15 15.1 610
PRACTITIONER PERSPECTIVE:
Statistics and Regression Analysis with Duxbury/Thomson Learning 611
15.2
15.3
15.4
15.5
The Simple Linear Regression Model 612Model and Assumptions 612
The Least-Squares Criterion 613
Determining the Least-Squares Regression Line 614
Point Estimates Using the Regression Line 615
Interval Estimation Using the Sample Regression LineThe Standard Error of Estimate 620
Confidence Interval for the Mean of /Given a Specific xValue 621
Prediction Interval for an Individual /Observation 622
Correlation Analysis 626The Coefficient of Correlation 627
The Coefficient of Determination 627
619
Estimation and Tests Regardingthe Sample Regression LineTesting the Coefficient of Correlation 631
Testing and Estimation for the Slope 632
631
STATISTICS IN ACTION 15.1:
The Beta Coefficient and Investment Decisions 633
The Analysis of Variance Perspective 634
15.6 Additional Topics in Regressionand Correlation Analysis 637Residual Analysis 637
Cautionary Notes 642
STATISTICS IN ACTION 15.2:
Major League Baseball: Does Money Really Win Games? 644
15.7 Summary 646
Multiple Regression and Correlation
Introduction ;
659
.16 16.1 660
PRACTITIONER PERSPECTIVE:
Multiple Regression with the NCAA 661
16.2 The Multiple Regression ModelModel and Assumptions 662
662
CONTENTS xvii
Determining the Sample Regression Equation GG3
Interpreting the Regression Equation 665
Point Estimates Using the Regression Equation 666
16.3 Interval Estimation in Multiple Regression 669The Multiple Standard Error of Estimate 670
Confidence Interval for the Conditional Mean of y 671
Prediction Interval for an Individual /Observation 672
16.4 Multiple Correlation Analysis 675The Coefficient of Multiple Determination 675
16.5 Significance Tests in Multiple Regressionand Correlation 678Testing the Significance of the Regression Equation 678
Testing the Partial Regression Coefficients 680
Interval Estimation for the Partial Regression Coefficients 681
16.6 Overview of the Computer Analysisand Interpretation 683A Summary of the Results 683
STATISTICS IN ACTION 16.1:
Predicting Holiday Traffic Fatalities 686
Residual Analysis 686
16.7 Additional Topics in Multiple Regressionand Correlation 693Including Qualitative Data: The Dummy Variable 693
Multicollinearity 695
16.8 Summary 697
Model Building 707
.17 17.1 Introduction 708
17.2 Polynomial Models with One QuantitativePredictor Variable 708The General Polynomial Model 710
PRACTITIONER PERSPECTIVE:
Model Building with Research International USA 710
First-Order Polynomial Model 711
Second-Order Polynomial Model 711
Third-Order Polynomial Model 712
17.3 Polynomial Models with Two QuantitativePredictor Variables 717First-Order Model with Two Variables 718
First-Order Model with an Interaction Term 718
Second-Order Model with Interaction 719
xviii CONTENTS
.18
17.4 Qualitative Variables 723Qualitative Variable Representing Two Possible Categories 724
Qualitative Variables Representing More Than Two Possible Categories 724
17.5 Data Transformations 728
17.6 Multicollinearity 731
17.7 Stepwise Regression 734
STATISTICS IN ACTION 17.1:
Stepwise Regression and the NFL Passer Rating 739
17.8 Selecting a Model 742
17.9 Summary 743
Models for Time Series and Forecasting 75118.1 Introduction 752
18.2 Time Series 752
PRACTITIONER PERSPECTIVE:
Retirees Depend on Cost-of-Living Adjustments to Fight Inflation 753
Components of a Time Series 754
STATISTICS IN ACTION 18.1:
Global Temperatures: A 100,000-Year Cycle 754
Fitting a Linear Trend Equation 756
Fitting a Quadratic Trend Equation 758
18.3 Smoothing Techniques 760The Moving Average 760
Exponential Smoothing 766
18.4 Seasonal Indexes 771The Ratio to Moving Average Method 772
Deseasonalizing the Time Series 774
18.5 Forecasting 777Forecasts Using the Trend Equation 778
Forecasting with Exponential Smoothing 778
Seasonal Indexes in Forecasting 779
18.6 Evaluating Alternative Models MAD and MSE 782
18.7 Autocorrelation, the Durbin-Watson Test,and Autoregressive Forecasting 785Autocorrelation and the Durbin-Watson Test 785
The Autoregressive Forecasting Model 789
18.8 Index Numbers 795The Consumer Price Index 796
CONTENTS xix
STATISTICS IN ACTION 18.2:
The CPI Time Machine 798
Other Indexes 798
Shifting the Base of an Index 799
18.9 Summary 800
PART SIX
Special TopicsDecision Theory 811
.19 19.1
19.2
Introduction 812
Structuring the Decision SituationAlternatives 813
813
PRACTITIONER PERSPECTIVE:
Making Decisions with CompAS Controls, Inc. 813
States of Nature 814
STATISTICS IN ACTION 19.1:
New Technology Makes Invention Hit Bottom 814
The Payoff Table 815
19.3 Non-Bayesian Decision Making 817Maximin 817
Maximax 817
Minimax Regret 818
19.4 Bayesian Decision Making 820Expected Payoff 821
The Expected Value of Perfect Information 822
STATISTICS IN ACTION 19.2:
Expected Payoff, Maximax, and the Lottery 823
19.5 The Opportunity Loss Approach 826
19.6 Incremental Analysis and Inventory Decisions
19.7 Summary 831
Appendix to Chapter 19:The Expected Value of Imperfect Information
827
833
Total Quality Management 839.20 20.1 840Introduction
What Is Quality? 840
PRACTITIONER PERSPECTIVE:
Practicing TQM at Ben ft Jerry's Homemade 841
xx CONTENTS
Why Is Quality Important? 842
Process Variation and Product Quality 843
20.2 A Historical Perspective and Defect Detection 844
20.3 The Emergence of Total Quality Management 845TQM Pioneers 846The Process Orientation 847
20.4 Practicing Total Quality Management 848"Kaizen" and TQM 848
Deming's 14 Points 848
The Quality Audit 849
Competitive Benchmarking 850
Just-in-Time Manufacturing 850
Worker Empowerment 851
STATISTICS IN ACTION 20.1:
Quality Circles and the "Suggestion Box" 852
Awards and the Recognition of Quality 852
20.5 Some Statistical Tools for Total Quality Management 853The Process Flow Chart 853
The Cause-and-Effect Diagram 853
The Pareto Diagram 855
The Check Sheet 855
Taguchi Methods 856
Designed Experiments 857
20.6 Statistical Process Control: The Concepts 858Types of Control Charts 858
The Control Chart Format 858
20.7 Control Charts for Variables 859Mean Charts 859
Construction of a Mean Chart 860
Range Charts 862
20.8 Control Charts for Attributes 868p-Charts 869
c-Charts 870
20.9 More on Computer-Assisted Statistical Process Control 877
20.10 Summary 879
Appendix A: Statistical Tables 887
Appendix B: Selected Answers 923
Index/Glossary 927
CONTENTS xxi
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