Answer the questions below

Read the Case Problem 3 (Selecting a Point and Shoot Digital Camera) presented at the end of chapter 14 in the textbook. Answer the following questions:

one using price as the independent variable, one using the number of megapixels as the independent variable, and one using weight as the independent variable. which of the three independent variables appears to be the best predictor of overall score?

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Statistics for
Business & Economics
14e
James J. Cochran
Thomas A. Williams
David R. Anderson
University of Alabama
Rochester Institute
of Technology
University of Cincinnati
Dennis J. Sweeney
Michael J. Fry
University of Cincinnati
Jeffrey D. Camm
University of Cincinnati
Jeffrey W. Ohlmann
Wake Forest University
University of Iowa
Australia Brazil Mexico Singapore United Kingdom United States
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Statistics for Business and Economics, 14e
David R. Anderson
Dennis J. Sweeney
Thomas A. Williams
Jeffrey D. Camm
James J. Cochran
Michael J. Fry
Jeffrey W. Ohlmann
© 2020, 2017 Cengage Learning, Inc.
Unless otherwise noted, all content is © Cengage.
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Brief Contents
ABOUT THE AUTHORS xxi
PREFACE xxv
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Chapter 20
Chapter 21
Chapter 22
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
Data and Statistics 1
Descriptive Statistics: Tabular and Graphical Displays 33
Descriptive Statistics: Numerical Measures 107
Introduction to Probability 177
Discrete Probability Distributions 223
Continuous Probability Distributions 281
Sampling and Sampling Distributions 319
Interval Estimation 373
Hypothesis Tests 417
Inference About Means and Proportions with
Two Populations 481
Inferences About Population Variances 525
Comparing Multiple Proportions, Test
of Independence and Goodness of Fit 553
Experimental Design and Analysis of Variance 597
Simple Linear Regression 653
Multiple Regression 731
Regression Analysis: Model Building 799
Time Series Analysis and Forecasting 859
Nonparametric Methods 931
Decision Analysis 981
Index Numbers 1013
Statistical Methods for Quality Control 1033
Sample Survey (MindTap Reader) 22-1
References and Bibliography 1068
Tables 1070
Summation Notation 1097
Answers to Even-Numbered Exercises (MindTap Reader)
Microsoft Excel 2016 and Tools for Statistical Analysis 1099
Computing p-Values with JMP and Excel 1107
Index
1111
Chapter 11
Chapter 12
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Contents
ABOUT THE AUTHORS xxi
PREFACE xxv
Data and Statistics   1
Statistics in Practice: Bloomberg Businessweek 2
1.1 Applications in Business and Economics 3
Accounting 3
Finance 3
Marketing 4
Production 4
Economics 4
Information Systems 4
1.2 Data 5
Elements, Variables, and Observations 5
Scales of Measurement 5
Categorical and Quantitative Data 7
Cross-Sectional and Time Series Data 8
1.3 Data Sources 10
Existing Sources 10
Observational Study 11
Experiment 12
Time and Cost Issues 13
Data Acquisition Errors 13
1.4 Descriptive Statistics 13
1.5 Statistical Inference 15
1.6 Analytics 16
1.7 Big Data and Data Mining 17
1.8 Computers and Statistical Analysis 19
1.9 Ethical Guidelines for Statistical Practice 19
Chapter 1
Summary 21
Glossary 21
Supplementary Exercises 22
Appendix 1.1 Opening and Saving DATA Files and Converting to Stacked
form with JMP 30
Appendix 1.2 Getting Started with R and RStudio (MindTap Reader)
Appendix 1.3 Basic Data Manipulation in R (MindTap Reader)
Descriptive Statistics: Tabular and Graphical
Displays  33
Statistics in Practice: Colgate-Palmolive Company 34
2.1 Summarizing Data for a Categorical Variable 35
Frequency Distribution 35
Relative Frequency and Percent Frequency Distributions 36
Bar Charts and Pie Charts 37
Chapter 2
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Contents
2.2 Summarizing Data for a Quantitative Variable 42
Frequency Distribution 42
Relative Frequency and Percent Frequency Distributions 44
Dot Plot 45
Histogram 45
Cumulative Distributions 47
Stem-and-Leaf Display 47
2.3 Summarizing Data for Two Variables Using Tables 57
Crosstabulation 57
Simpson’s Paradox 59
2.4  Summarizing Data for Two Variables Using Graphical
Displays 65
Scatter Diagram and Trendline 65
Side-by-Side and Stacked Bar Charts 66
2.5  Data Visualization: Best Practices in Creating Effective
Graphical Displays 71
Creating Effective Graphical Displays 71
Choosing the Type of Graphical Display 72
Data Dashboards 73
Data Visualization in Practice: Cincinnati Zoo
and Botanical Garden 75
Summary 77
Glossary 78
Key Formulas 79
Supplementary Exercises 80
Case Problem 1: Pelican Stores 85
Case Problem 2: Movie Theater Releases 86
Case Problem 3: Queen City 87
Case Problem 4: Cut-Rate Machining, Inc. 88
Appendix 2.1 Creating Tabular and Graphical Presentations with JMP 90
Appendix 2.2 Creating Tabular and Graphical Presentations
with Excel 93
Appendix 2.3 Creating Tabular and Graphical Presentations with R
(MindTap Reader)
Descriptive Statistics: Numerical Measures   107
Statistics in Practice: Small Fry Design 108
3.1  Measures of Location 109
Mean 109
Weighted Mean 111
Median 112
Geometric Mean 113
Mode 115
Percentiles 115
Quartiles 116
Chapter 3
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vi
Contents
3.2  Measures of Variability 122
Range 123
Interquartile Range 123
Variance 123
Standard Deviation 125
Coefficient of Variation 126
3.3  Measures of Distribution Shape, Relative Location,
and Detecting Outliers 129
Distribution Shape 129
z-Scores 130
Chebyshev’s Theorem 131
Empirical Rule 132
Detecting Outliers 134
3.4  Five-Number Summaries and Boxplots 137
Five-Number Summary 138
Boxplot 138
Comparative Analysis Using Boxplots 139
3.5  Measures of Association Between Two Variables 142
Covariance 142
Interpretation of the Covariance 144
Correlation Coefficient 146
Interpretation of the Correlation Coefficient 147
3.6  Data Dashboards: Adding Numerical Measures to
Improve Effectiveness 150
Summary 153
Glossary 154
Key Formulas 155
Supplementary Exercises 156
Case Problem 1: Pelican Stores 162
Case Problem 2: Movie Theater Releases 163
Case Problem 3: Business Schools of Asia-Pacific 164
Case Problem 4: Heavenly Chocolates Website Transactions 164
Case Problem 5: African Elephant Populations 166
Appendix 3.1 Descriptive Statistics with JMP 168
Appendix 3.2 Descriptive Statistics with Excel 171
Appendix 3.3 Descriptive Statistics with R (MindTap Reader)
Introduction to Probability   177
Statistics in Practice: National Aeronautics and Space
Administration 178
4.1  Random Experiments, Counting Rules,
and Assigning Probabilities 179
Counting Rules, Combinations, and Permutations 180
Assigning Probabilities 184
Probabilities for the KP&L Project 185
4.2 Events and Their Probabilities 189
Chapter 4
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Contents
4.3  Some Basic Relationships of Probability 193
Complement of an Event 193
Addition Law 194
4.4  Conditional Probability 199
Independent Events 202
Multiplication Law 202
4.5  Bayes’ Theorem 207
Tabular Approach 210
Summary 212
Glossary 213
Key Formulas 214
Supplementary Exercises 214
Case Problem 1: Hamilton County Judges 219
Case Problem 2: Rob’s Market 221
Discrete Probability Distributions   223
Statistics in Practice: Voter Waiting Times in Elections 224
5.1  Random Variables 225
Discrete Random Variables 225
Continuous Random Variables 225
5.2  Developing Discrete Probability Distributions 228
5.3  Expected Value and Variance 233
Expected Value 233
Variance 233
5.4  Bivariate Distributions, Covariance, and Financial Portfolios 238
A Bivariate Empirical Discrete Probability Distribution 238
Financial Applications 241
Summary 244
5.5  Binomial Probability Distribution 247
A Binomial Experiment 248
Martin Clothing Store Problem 249
Using Tables of Binomial Probabilities 253
Expected Value and Variance for the Binomial Distribution 254
5.6  Poisson Probability Distribution 258
An Example Involving Time Intervals 259
An Example Involving Length or Distance Intervals 260
5.7  Hypergeometric Probability Distribution 262
Chapter 5
Summary 265
Glossary 266
Key Formulas 266
Supplementary Exercises 268
Case Problem 1: Go Bananas! Breakfast Cereal 272
Case Problem 2: McNeil’s Auto Mall 272
Case Problem 3: Grievance Committee at Tuglar Corporation 273
Appendix 5.1 Discrete Probability Distributions with JMP 275
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viii
Contents
Appendix 5.2 Discrete Probability Distributions with Excel 278
Appendix 5.3 Discrete Probability Distributions with R (MindTap Reader)
Continuous Probability Distributions 281
Statistics in Practice: Procter & Gamble 282
6.1  Uniform Probability Distribution 283
Area as a Measure of Probability 284
6.2  Normal Probability Distribution 287
Normal Curve 287
Standard Normal Probability Distribution 289
Computing Probabilities for Any Normal Probability
Distribution 294
Grear Tire Company Problem 294
6.3  Normal Approximation of Binomial Probabilities 299
6.4  Exponential Probability Distribution 302
Computing Probabilities for the Exponential
Distribution 302
Relationship Between the Poisson and Exponential
Distributions 303
Summary 305
Glossary 305
Key Formulas 306
Supplementary Exercises 306
Case Problem 1: Specialty Toys 309
Case Problem 2: Gebhardt Electronics 311
Appendix 6.1 Continuous Probability Distributions with JMP 312
Appendix 6.2 Continuous Probability Distributions with Excel 317
Appendix 6.3 Continuous Probability Distribution with R
(MindTap Reader)
Chapter 6
Sampling and Sampling Distributions 319
Statistics in Practice: Meadwestvaco Corporation 320
7.1  The Electronics Associates Sampling Problem 321
7.2 Selecting a Sample 322
Sampling from a Finite Population 322
Sampling from an Infinite Population 324
7.3  Point Estimation 327
Practical Advice 329
7.4  Introduction to Sampling Distributions 331
7.5 Sampling Distribution of x 333
Expected Value of x 334
Standard Deviation of x 334
Form of the Sampling Distribution of x 335
Sampling Distribution of x for the EAI Problem 337
Practical Value of the Sampling Distribution of x 338
Relationship Between the Sample Size and the Sampling
Distribution of x 339
Chapter 7
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Contents
7.6 Sampling Distribution of p 343
Expected Value of p 344
Standard Deviation of p 344
Form of the Sampling Distribution of p 345
Practical Value of the Sampling Distribution of p 345
7.7 Properties of Point Estimators 349
Unbiased 349
Efficiency 350
Consistency 351
7.8 Other Sampling Methods 351
Stratified Random Sampling 352
Cluster Sampling 352
Systematic Sampling 353
Convenience Sampling 353
Judgment Sampling 354
7.9 Big Data and Standard Errors of Sampling Distributions 354
Sampling Error 354
Nonsampling Error 355
Big Data 356
Understanding What Big Data Is 356
Implications of Big Data for Sampling Error 357
Summary 360
Glossary 361
Key Formulas 362
Supplementary Exercises 363
Case Problem: Marion Dairies 366
Appendix 7.1 The Expected Value and Standard Deviation of x 367
Appendix 7.2 Random Sampling with JMP 368
Appendix 7.3 Random Sampling with Excel 371
Appendix 7.4 Random Sampling with R (MindTap Reader)
Interval Estimation  373
Statistics in Practice: Food Lion 374
8.1 Population Mean: s Known 375
Margin of Error and the Interval Estimate 375
Practical Advice 379
8.2 Population Mean: s Unknown 381
Margin of Error and the Interval Estimate 382
Practical Advice 385
Using a Small Sample 385
Summary of Interval Estimation Procedures 386
8.3  Determining the Sample Size 390
8.4  Population Proportion 393
Determining the Sample Size 394
Chapter 8
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x
Contents
8.5 Big Data and Confidence Intervals 398
Big Data and the Precision of Confidence Intervals 398
Implications of Big Data for Confidence Intervals 399
Summary 401
Glossary 402
Key Formulas 402
Supplementary Exercises 403
Case Problem 1: Young Professional Magazine 406
Case Problem 2: Gulf Real Estate Properties 407
Case Problem 3: Metropolitan Research, Inc. 409
Appendix 8.1 Interval Estimation with JMP 410
Appendix 8.2 Interval Estimation Using Excel 413
Appendix 8.3 Interval Estimation with R (MindTap Reader)
Hypothesis Tests  417
Statistics in Practice: John Morrell & Company 418
9.1 Developing Null and Alternative Hypotheses 419
The Alternative Hypothesis as a Research Hypothesis 419
The Null Hypothesis as an Assumption to Be Challenged 420
Summary of Forms for Null and Alternative Hypotheses 421
9.2 Type I and Type II Errors 422
9.3 Population Mean: s Known 425
One-Tailed Test 425
Two-Tailed Test 430
Summary and Practical Advice 433
Relationship Between Interval Estimation and
Hypothesis Testing 434
9.4 Population Mean: s Unknown 439
One-Tailed Test 439
Two-Tailed Test 440
Summary and Practical Advice 441
9.5 Population Proportion 445
Summary 447
9.6 Hypothesis Testing and Decision Making 450
9.7 Calculating the Probability of Type II Errors 450
9.8  Determining the Sample Size for a Hypothesis Test
About a Population Mean 455
9.9 Big Data and Hypothesis Testing 459
Big Data, Hypothesis Testing, and p Values 459
Implications of Big Data in Hypothesis Testing 460
Summary 462
Glossary 462
Key Formulas 463
Supplementary Exercises 463
Case Problem 1: Quality Associates, Inc. 467
Chapter 9
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Contents
xi
Case Problem 2: Ethical Behavior of Business Students
at Bayview University 469
Appendix 9.1 Hypothesis Testing with JMP 471
Appendix 9.2 Hypothesis Testing with Excel 475
Appendix 9.3 Hypothesis Testing with R (MindTap Reader)
Inference About Means and Proportions with
Two Populations  481
Statistics in Practice: U.S. Food and Drug Administration 482
10.1  Inferences About the Difference Between Two
Population Means: s1 and s2 Known 483
Interval Estimation of m1 − m2 483
Hypothesis Tests About m1 − m2 485
Practical Advice 487
10.2  Inferences About the Difference Between Two
Population Means: s1 and s2 Unknown 489
Interval Estimation of m1 − m2 489
Hypothesis Tests About m1 − m2 491
Practical Advice 493
10.3  Inferences About the Difference Between Two
Population Means: Matched Samples 497
10.4  Inferences About the Difference Between Two Population
Proportions 503
Interval Estimation of p1 − p2 503
Hypothesis Tests About p1 − p2 505
Summary 509
Glossary 509
Key Formulas 509
Supplementary Exercises 511
Case Problem: Par, Inc. 514
Appendix 10.1 Inferences About Two Populations with JMP 515
Appendix 10.2 Inferences About Two Populations with Excel 519
Appendix 10.3 Inferences about Two Populations with R (MindTap Reader)
Chapter 10
Inferences About Population Variances   525
Statistics in Practice: U.S. Government Accountability Office 526
11.1  Inferences About a Population Variance 527
Interval Estimation 527
Hypothesis Testing 531
11.2  Inferences About Two Population Variances 537
Chapter 11
Summary 544
Key Formulas 544
Supplementary Exercises 544
Case Problem 1: Air Force Training Program 546
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Contents
Case Problem 2: Meticulous Drill & Reamer 547
Appendix 11.1 Population Variances with JMP 549
Appendix 11.2 Population Variances with Excel 551
Appendix 11.3 Population Variances with R (MindTap Reader)
 omparing Multiple Proportions, Test of
C
Independence and Goodness of Fit   553
Statistics in Practice: United Way 554
12.1  Testing the Equality of Population Proportions
for Three or More Populations 555
A Multiple Comparison Procedure 560
12.2  Test of Independence 565
12.3  Goodness of Fit Test 573
Multinomial Probability Distribution 573
Normal Probability Distribution 576
Summary 582
Glossary 582
Key Formulas 583
Supplementary Exercises 583
Case Problem 1: A Bipartisan Agenda for Change 587
Case Problem 2: Fuentes Salty Snacks, Inc. 588
Case Problem 3: Fresno Board Games 588
Appendix 12.1 Chi-Square Tests with JMP 590
Appendix 12.2 Chi-Square Tests with Excel 593
Appendix 12.3 Chi-Squared Tests with R (MindTap Reader)
Chapter 12
Experimental Design and Analysis
of Variance  597
Statistics in Practice: Burke Marketing Services, Inc. 598
13.1  An Introduction to Experimental Design
and Analysis of Variance 599
Data Collection 600
Assumptions for Analysis of Variance 601
Analysis of Variance: A Conceptual Overview 601
13.2  Analysis of Variance and the Completely
Randomized Design 604
Between-Treatments Estimate of Population Variance 605
Within-Treatments Estimate of Population Variance 606
Comparing the Variance Estimates: The F Test 606
ANOVA Table 608
Computer Results for Analysis of Variance 609
Testing for the Equality of k Population Means:
An Observational Study 610
13.3  Multiple Comparison Procedures 615
Fisher’s LSD 615
Type I Error Rates 617
Chapter 13
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xiii
13.4  Randomized Block Design 621
Air Traffic Controller Stress Test 621
ANOVA Procedure 623
Computations and Conclusions 623
13.5  Factorial Experiment 627
ANOVA Procedure 629
Computations and Conclusions 629
Summary 635
Glossary 635
Key Formulas 636
Supplementary Exercises 638
Case Problem 1: Wentworth Medical Center 643
Case Problem 2: Compensation for Sales Professionals 644
Case Problem 3: Touristopia Travel 644
Appendix 13.1 Analysis of Variance with JMP 646
Appendix 13.2 Analysis of Variance with Excel 649
Appendix 13.3 Analysis Variance with R (MindTap Reader)
Chapter 14
Simple Linear Regression   653
Statistics in Practice: Alliance Data Systems 654
14.1  Simple Linear Regression Model 655
Regression Model and Regression Equation 655
Estimated Regression Equation 656
14.2  Least Squares Method 658
14.3  Coefficient of Determination 668
Correlation Coefficient 671
14.4  Model Assumptions 675
14.5  Testing for Significance 676
Estimate of s2 676
t Test 677
Confidence Interval for b1 679
F Test 679
Some Cautions About the Interpretation of Significance Tests 681
14.6  Using the Estimated Regression Equation
for Estimation and Prediction 684
Interval Estimation 685
Confidence Interval for the Mean Value of y 685
Prediction Interval for an Individual Value of y 686
14.7  Computer Solution 691
14.8  Residual Analysis: Validating Model Assumptions 694
Residual Plot Against x 695
Residual Plot Against ŷ 697
Standardized Residuals 698
Normal Probability Plot 699
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Contents
14.9  Residual Analysis: Outliers and Influential Observations 703
Detecting Outliers 703
Detecting Influential Observations 704
14.10  Practical Advice: Big Data and Hypothesis Testing in Simple Linear
Regression 710
Summary 711
Glossary 711
Key Formulas 712
Supplementary Exercises 714
Case Problem 1: Measuring Stock Market Risk 721
Case Problem 2: U.S. Department of Transportation 721
Case Problem 3: Selecting a Point-and-Shoot Digital Camera 722
Case Problem 4: Finding the Best Car Value 723
Case Problem 5: Buckeye Creek Amusement Park 724
Appendix 14.1 Calculus-Based Derivation of Least Squares Formulas 726
Appendix 14.2 A Test for Significance Using Correlation 727
Appendix 14.3 Simple Linear Regression with JMP 727
Appendix 14.4 Regression Analysis with Excel 728
Appendix 14.5 Simple Linear Regression with R (MindTap Reader)
Multiple Regression  731
Statistics in Practice: 84.51° 732
15.1  Multiple Regression Model 733
Regression Model and Regression Equation 733
Estimated Multiple Regression Equation 733
15.2  Least Squares Method 734
An Example: Butler Trucking Company 735
Note on Interpretation of Coefficients 737
15.3 Multiple Coefficient of Determination 743
15.4 Model Assumptions 746
15.5 Testing for Significance 747
F Test 747
t Test 750
Multicollinearity 750
15.6  Using the Estimated Regression Equation
for Estimation and Prediction 753
15.7 Categorical Independent Variables 755
An Example: Johnson Filtration, Inc. 756
Interpreting the Parameters 758
More Complex Categorical Variables 760
15.8 Residual Analysis 764
Detecting Outliers 766
Studentized Deleted Residuals and Outliers 766
Influential Observations 767
Using Cook’s Distance Measure to Identify
Influential Observations 767
Chapter 15
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Contents
15.9  Logistic Regression 771
Logistic Regression Equation 772
Estimating the Logistic Regression Equation 773
Testing for Significance 774
Managerial Use 775
Interpreting the Logistic Regression Equation 776
Logit Transformation 778
15.10  Practical Advice: Big Data and Hypothesis Testing
in Multiple Regression   782
Summary 783
Glossary 783
Key Formulas 784
Supplementary Exercises 786
Case Problem 1: Consumer Research, Inc. 790
Case Problem 2: Predicting Winnings for NASCAR Drivers 791
Case Problem 3: Finding the Best Car Value 792
Appendix 15.1 Multiple Linear Regression with JMP 794
Appendix 15.2 Logistic Regression with JMP 796
Appendix 15.3 Multiple Regression with Excel 797
Appendix 15.4 Multiple Linear Regression with R (MindTap Reader)
Appendix 15.5 Logistics Regression with R (MindTap Reader)
Regression Analysis: Model Building   799
Statistics in Practice: Monsanto Company 800
16.1  General Linear Model 801
Modeling Curvilinear Relationships 801
Interaction 805
Transformations Involving the Dependent Variable 807
Nonlinear Models That Are Intrinsically Linear 812
16.2 Determining When to Add or Delete Variables 816
General Case 818
Use of p-Values 819
16.3 Analysis of a Larger Problem 822
16.4  Variable Selection Procedures 826
Stepwise Regression 826
Forward Selection 828
Backward Elimination 828
Best-Subsets Regression 828
Making the Final Choice 829
16.5  Multiple Regression Approach to Experimental Design 832
16.6 Autocorrelation and the Durbin-Watson Test 836
Chapter 16
Summary 840
Glossary 841
Key Formulas 841
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Contents
Supplementary Exercises 841
Case Problem 1: Analysis of LPGA Tour Statistics 845
Case Problem 2: Rating Wines from the Piedmont Region of Italy 846
Appendix 16.1 Variable Selection Procedures with JMP 848
Appendix 16.2 Variable Selection Procedures with R (MindTap Reader)
Chapter 17
Time Series Analysis and Forecasting   859
Statistics in Practice: Nevada Occupational Health Clinic 860
17.1 Time Series Patterns 861
Horizontal Pattern 861
Trend Pattern 863
Seasonal Pattern 863
Trend and Seasonal Pattern 864
Cyclical Pattern 864
Selecting a Forecasting Method 866
17.2 Forecast Accuracy 867
17.3 Moving Averages and Exponential Smoothing 872
Moving Averages 872
Weighted Moving Averages 874
Exponential Smoothing 875
17.4 Trend Projection 881
Linear Trend Regression 882
Nonlinear Trend Regression 886
17.5 Seasonality and Trend 891
Seasonality Without Trend 892
Seasonality and Trend 894
Models Based on Monthly Data 897
17.6 Time Series Decomposition 900
Calculating the Seasonal Indexes 902
Deseasonalizing the Time Series 905
Using the Deseasonalized Time Series to Identify Trend 905
Seasonal Adjustments 907
Models Based on Monthly Data 908
Cyclical Component 908
Summary 910
Glossary 911
Key Formulas 912
Supplementary Exercises 913
Case Problem 1: Forecasting Food and Beverage Sales 917
Case Problem 2: Forecasting Lost Sales 918
Appendix 17.1 Forecasting with JMP 920
Appendix 17.2 Forecasting with Excel 926
Appendix 17.3 Forecasting with R (MindTap Reader)
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Contents
Nonparametric Methods  931
Statistics in Practice: West Shell Realtors 932
18.1 Sign Test 933
Hypothesis Test About a Population Median 933
Hypothesis Test with Matched Samples 938
18.2 Wilcoxon Signed-Rank Test 941
18.3 Mann-Whitney-Wilcoxon Test 947
18.4 Kruskal-Wallis Test 956
18.5 Rank Correlation 961
Chapter 18
Summary 966
Glossary 966
Key Formulas 967
Supplementary Exercises 968
Case Problem: RainOrShine.Com 971
Appendix 18.1 Nonparametric Methods with JMP 972
Appendix 18.2 Nonparametric Methods with Excel 979
Appendix 18.3 Nonparametric Methods with R (MindTap Reader)
Decision Analysis  981
Statistics in Practice: Ohio Edison Company 982
19.1 Problem Formulation 983
Payoff Tables 983
Decision Trees 984
19.2 Decision Making with Probabilities 985
Expected Value Approach 985
Expected Value of Perfect Information 987
19.3 Decision Analysis with Sample Information 992
Decision Tree 993
Decision Strategy 994
Expected Value of Sample Information 998
19.4  Computing Branch Probabilities Using Bayes’ Theorem 1002
Summary 1006
Glossary 1007
Key Formulas 1008
Supplementary Exercises 1008
Case Problem 1: Lawsuit Defense Strategy 1010
Case Problem 2: Property Purchase Strategy 1011
Chapter 19
Index Numbers  1013
Statistics in Practice: U.S. Department of Labor, Bureau
of Labor Statistics 1014
20.1 Price Relatives 1014
20.2 Aggregate Price Indexes 1015
Chapter 20
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xvii
xviii
Contents
20.3  Computing an Aggregate Price Index from Price Relatives 1019
20.4 Some Important Price Indexes 1021
Consumer Price Index 1021
Producer Price Index 1021
Dow Jones Averages 1022
20.5 Deflating a Series by Price Indexes 1023
20.6  Price Indexes: Other Considerations 1026
Selection of Items 1026
Selection of a Base Period 1026
Quality Changes 1027
20.7  Quantity Indexes 1027
Summary 1029
Glossary 1029
Key Formulas 1029
Supplementary Exercises 1030
 tatistical Methods for Quality Control   1033
S
Statistics in Practice: Dow Chemical Company 1034
21.1 Philosophies and Frameworks 1035
Malcolm Baldrige National Quality Award 1036
ISO 9000 1036
Six Sigma 1036
Quality in the Service Sector 1038
21.2  Statistical Process Control 1039
Control Charts 1040
x Chart: Process Mean and Standard Deviation Known 1041
x Chart: Process Mean and Standard Deviation Unknown 1043
R Chart 1045
p Chart 1046
np Chart 1049
Interpretation of Control Charts 1049
21.3 Acceptance Sampling 1052
KALI, Inc.: An Example of Acceptance Sampling 1053
Computing the Probability of Accepting a Lot 1054
Selecting an Acceptance Sampling Plan 1056
Multiple Sampling Plans 1057
Summary 1059
Glossary 1060
Key Formulas 1060
Supplementary Exercises 1061
Appendix 21.1 Control Charts with JMP 1064
Appendix 21.2 Control Charts with R (MindTap Reader)
Chapter 21
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xix
Contents
Chapter 22
Sample Survey (MindTap Reader)   22-1
Statistics in Practice: Duke Energy 22-2
22.1  Terminology Used in Sample Surveys 22-2
22.2 Types of Surveys and Sampling Methods 22-3
22.3 Survey Errors 22-5
Nonsampling Error 22-5
Sampling Error 22-5
22.4 Simple Random Sampling 22-6
Population Mean 22-6
Population Total 22-7
Population Proportion 22-8
Determining the Sample Size 22-9
22.5 Stratified Simple Random Sampling 22-12
Population Mean 22-12
Population Total 22-14
Population Proportion 22-15
Determining the Sample Size 22-16
22.6 Cluster Sampling 22-21
Population Mean 22-23
Population Total 22-25
Population Proportion 22-25
Determining the Sample Size 22-27
22.7 Systematic Sampling 22-29
Summary 22-29
Glossary 22-30
Key Formulas 22-30
Supplementary Exercises 22-34
Case Problem: Medicament’s Predicament 22-36
Appendix A  References and Bibliography  1068
Appendix B
Tables  1070
Appendix C
Summation Notation  1097
Appendix D   Answers to Even-Numbered Exercises (MindTap Reader)  
Appendix E   Microsoft Excel 2016 and Tools for Statistical Analysis   1099
Appendix F  Computing p-Values with JMP and Excel   1107
Index 1111
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About the Authors
David R. Anderson. David R. Anderson is Professor Emeritus of Quantitative Analysis
in the College of Business Administration at the University of Cincinnati. Born in Grand
Forks, North Dakota, he earned his B.S., M.S., and Ph.D. degrees from Purdue University.
Professor ­Anderson has served as Head of the Department of Quantitative Analysis and
Operations Management and as Associate Dean of the College of Business Administration
at the University of Cincinnati. In addition, he was the coordinator of the College’s first
Executive Program.
At the University of Cincinnati, Professor Anderson has taught introductory statistics
for business students as well as graduate-level courses in regression analysis, multivariate analysis, and management science. He has also taught statistical courses at the Department of Labor in Washington, D.C. He has been honored with nominations and awards for
­excellence in teaching and excellence in service to student organizations.
Professor Anderson has coauthored 10 textbooks in the areas of statistics, management
science, linear programming, and production and operations management. He is an active
consultant in the field of sampling and statistical methods.
Dennis J. Sweeney. Dennis J. Sweeney is Professor Emeritus of Quantitative Analysis and
Founder of the Center for Productivity Improvement at the University of Cincinnati. Born in
Des Moines, Iowa, he earned a B.S.B.A. degree from Drake University and his M.B.A. and
D.B.A. degrees from Indiana University, where he was an NDEA Fellow. Professor Sweeney
has worked in the management science group at Procter & Gamble and spent a year as a
visiting professor at Duke University. Professor Sweeney served as Head of the Department
of Quantitative Analysis and as Associate Dean of the College of B
­ usiness ­Administration at
the University of Cincinnati.
Professor Sweeney has published more than 30 articles and monographs in the area of
management science and statistics. The National Science Foundation, IBM, Procter & Gamble, Federated Department Stores, Kroger, and Cincinnati Gas & Electric have funded his
research, which has been published in Management Science, Operations Research, Mathematical Programming, Decision Sciences, and other journals.
Professor Sweeney has coauthored 10 textbooks in the areas of statistics, management
science, linear programming, and production and operations management.
Thomas A. Williams. Thomas A. Williams is Professor Emeritus of Management S
­ cience
in the College of Business at Rochester Institute of Technology. Born in Elmira, New York,
he earned his B.S. degree at Clarkson University. He did his graduate work at ­Rensselaer
Polytechnic Institute, where he received his M.S. and Ph.D. degrees.
Before joining the College of Business at RIT, Professor Williams served for seven years
as a faculty member in the College of Business Administration at the University of Cincinnati, where he developed the undergraduate program in Information Systems and then served
as its coordinator. At RIT he was the first chairman of the Decision Sciences Department. He
teaches courses in management science and statistics, as well as graduate courses in regression and decision analysis.
Professor Williams is the coauthor of 11 textbooks in the areas of management s­ cience,
statistics, production and operations management, and mathematics. He has been a consultant for numerous Fortune 500 companies and has worked on projects ranging from the use
of data analysis to the development of large-scale regression models.
Jeffrey D. Camm. Jeffrey D. Camm is the Inmar Presidential Chair and Associate Dean of
Analytics in the School of Business at Wake Forest University. Born in Cincinnati, Ohio, he
holds a B.S. from Xavier University (Ohio) and a Ph.D. from Clemson University. Prior to
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xxii
About the Authors
joining the faculty at Wake Forest, he was on the faculty of the University of Cincinnati. He
has also been a visiting scholar at Stanford University and a visiting professor of business
administration at the Tuck School of Business at Dartmouth College.
Dr. Camm has published over 40 papers in the general area of optimization applied to
problems in operations management and marketing. He has published his research in ­Science,
Management Science, Operations Research, Interfaces, and other professional journals. Dr.
Camm was named the Dornoff Fellow of Teaching Excellence at the University of Cincinnati and he was the 2006 recipient of the INFORMS Prize for the Teaching of Operations
Research Practice. A firm believer in practicing what he preaches, he has served as an operations research consultant to numerous companies and government agencies. From 2005 to
2010 he served as editor-in-chief of Interfaces. In 2017, he was named an INFORMS Fellow.
James J. Cochran. James J. Cochran is Professor of Applied Statistics and the RogersSpivey Faculty Fellow at the University of Alabama. Born in Dayton, Ohio, he earned his
B.S., M.S., and M.B.A. degrees from Wright State University and a Ph.D. from the ­University
of Cincinnati. He has been at the University of Alabama since 2014 and has been a visiting
scholar at Stanford University, Universidad de Talca, the University of South ­Africa, and
Pole Universitaire Leonard de Vinci.
Professor Cochran has published over 40 papers in the development and application of
operations research and statistical methods. He has published his research in Management
Science, The American Statistician, Communications in Statistics—Theory and Methods,
Annals of operations Research, European Journal of Operational Research, Journal of Combinatorial Optimization. Interfaces, Statistics and Probability Letters, and other professional
journals. He was the 2008 recipient of the INFORMS Prize for the Teaching of Operations
Research Practice and the 2010 recipient of the Mu Sigma Rho Statistical Education Award.
Professor Cochran was elected to the International Statistics Institute in 2005 and named a
Fellow of the American Statistical Association in 2011. He received the Founders Award
in 2014 and the Karl E. Peace Award in 2015 from the American Statistical Association. In
2017 he received the American Statistical Association’s Waller Distinguished Teaching Career Award and was named a Fellow of INFORMS, and in 2018 he received the INFORMS
President’s Award.
A strong advocate for effective statistics and operations research education as a means
of improving the quality of applications to real problems, Professor Cochran has organized
and chaired teaching effectiveness workshops in Montevideo, Uruguay; Cape Town, South
Africa; Cartagena, Colombia; Jaipur, India; Buenos Aires, Argentina; Nairobi, Kenya; Buea,
Cameroon; Kathmandu, Nepal; Osijek, Croatia; Havana, Cuba; Ulaanbaatar, Mongolia; and
Chis̹inău, Moldova. He has served as an operations research consultant to numerous companies and not-for-profit organizations. He served as editor-in-chief of INFORMS Transactions
on Education from 2006 to 2012 and is on the editorial board of Interfaces, International
Transactions in Operational Research, and Significance.
Michael J. Fry. Michael J. Fry is Professor of Operations, Business Analytics, and Information Systems and Academic Director of the Center for Business Analytics in the Carl
H. Lindner College of Business at the University of Cincinnati. Born in Killeen, Texas, he
earned a BS from Texas A&M University and M.S.E. and Ph.D. degrees from the University
of Michigan. He has been at the University of Cincinnati since 2002, where he was previously Department Head and has been named a Lindner Research Fellow. He has also been a
visiting professor at the Samuel Curtis Johnson Graduate School of Management at Cornell
University and the Sauder School of Business at the University of British Columbia.
Professor Fry has published more than 25 research papers in journals such as Operations
Research, M&SOM, Transportation Science, Naval Research Logistics, IIE Transactions,
Critical Care Medicine and Interfaces. His research interests are in applying quantitative
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About the Authors
xxiii
management methods to the areas of supply chain analytics, sports analytics, and public-­
policy operations. He has worked with many different organizations for his research, including Dell, Inc., Starbucks Coffee Company, Great American Insurance Group, the Cincinnati
Fire Department, the State of Ohio Election Commission, the Cincinnati Bengals, and the
Cincinnati Zoo & Botanical Garden. He was named a finalist for the Daniel H. Wagner Prize
for Excellence in Operations Research Practice, and he has been recognized for both his
research and teaching excellence at the University of Cincinnati.
Jeffrey W. Ohlmann. Jeffrey W. Ohlmann is Associate Professor of Management Sciences and Huneke Research Fellow in the Tippie College of Business at the University of
Iowa. Born in Valentine, Nebraska, he earned a B.S. from the University of Nebraska, and
MS and Ph.D. degrees from the University of Michigan. He has been at the University of
Iowa since 2003.
Professor Ohlmann’s research on the modeling and solution of decision-making problems
has produced more than 20 research papers in journals such as Operations Research, Mathematics of Operations Research, INFORMS Journal on Computing, Transportation Science,
the European Journal of Operational Research, and Interfaces. He has collaborated with
companies such as Transfreight, LeanCor, Cargill, the Hamilton County Board of Elections,
and three National Football League franchises. Because of the relevance of his work to industry, he was bestowed the George B. Dantzig Dissertation Award and was recognized as
a finalist for the Daniel H. Wagner Prize for Excellence in Operations Research Practice.
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Preface
T
his text is the 14th edition of STATISTICS FOR BUSINESS AND ECONOMICS.
  
In this edition, we include procedures for statistical analysis using Excel 2016 and JMP
Student Edition 14. In MindTap Reader, we also include instructions for using the exceptionally
popular open-source language R to perform statistical analysis. We are excited to introduce
two new coauthors, Michael J. Fry of the University of Cincinnati and Jeffrey W. Ohlmann of
the University of Iowa. Both are accomplished teachers and researchers. More details on their
backgrounds may be found in the About the Authors section.
The remainder of this preface describes the authors’ objectives in writing STATISTICS
FOR BUSINESS AND ECONOMICS and the major changes that were made in developing
the 14th edition. The purpose of the text is to give students, primarily those in the fields of
business administration and economics, a conceptual introduction to the field of statistics
and its many applications. The text is applications-oriented and written with the needs of
the nonmathematician in mind; the mathematical prerequisite is understanding of algebra.
Applications of data analysis and statistical methodology are an integral part of the organization and presentation of the text material. The discussion and development of each
technique is presented in an application setting, with the statistical results providing insights
to decisions and solutions to problems.
Although the book is applications oriented, we have taken care to provide sound methodological development and to use notation that is generally accepted for the topic being
covered. Hence, students will find that this text provides good preparation for the study of
more advanced statistical material. A bibliography to guide further study is included as an
appendix.
The text introduces the student to the software packages of JMP Student Edition 14e and
­Microsoft® ­Office ­Excel 2016 and emphasizes the role of computer software in the application
of ­statistical analysis. JMP is illustrated as it is one of the leading statistical software packages
for both ­education and statistical practice. Excel is not a statistical software package, but the
wide availability and use of Excel make it important for students to understand the statistical
­capabilities of this package. JMP and Excel procedures are provided in a­ ppendices so that instructors have the flexibility of using as much computer emphasis as desired for the course.
MindTap Reader includes appendices for using R for statistical analysis. R is an open-source
programming language that is widely used in practice to perform statistical analysis. The use of
R typically requires more training than the use of software such as JMP or Excel, but the software is extremely powerful. To ease students’ introduction to the R language, we also use
­RStudio which provides an integrated development environment for R.
Changes in the 14th Edition
We appreciate the acceptance and positive response to the previous editions of Statistics for
Business and Economics. Accordingly, in making modifications for this new edition, we
have maintained the presentation style and readability of those editions. There have been
many changes made throughout the text to enhance its educational effectiveness. The most
substantial changes in the new edition are summarized here.
Content Revisions
 oftware. In addition to step-by-step instructions in the software appendices for
S
Excel 2016, we also provide instructions for JMP Student Edition 14 and R. This
provides students exposure to and experience with the current versions of several of
the most commonly used software for statistical analysis in business. Excel 2016 and
JMP appendices are contained within the textbook chapters, while R appendices are
provided in MindTap Reader. In this latest edition, we no longer provide discussion of
the use of Minitab.
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xxvi
Preface
 ase Problems. We have added 12 new case problems in this edition; the total numC
ber of cases is now 42. One new case on graphical display has been added to Chapter
2. Two new cases using discrete probability distributions have been added to Chapter
5, and one new case using continuous probability distributions has been added to
Chapter 6. A new case on hypothesis testing has been added to Chapter 11, and two
new cases on testing proportions have been added to Chapter 12. The Chapter 16
case on regression model building has been updated. A new case utilizing nonparametric procedures has been added to Chapter 18, and a new case on sample survey
has been added to Chapter 22. The 42 case problems in this book provide students
the opportunity to work on more complex problems, analyze larger data sets, and
prepare managerial reports based on the results of their analyses.
 xamples and Exercises Based on Real Data. In this edition, we have added headers
E
to all Applications exercises to make the application of each problem more obvious.
We continue to make a substantial effort to update our text examples and exercises with
the most current real data and referenced sources of statistical information. We have
added more than 160 new examples and exercises based on real data and referenced
sources. Using data from sources also used by The Wall Street Journal, USA Today,
The Financial Times, and others, we have drawn from actual studies and applications
to develop explanations and create exercises that demonstrate the many uses of statistics in business and economics. We believe that the use of real data from interesting
and relevant problems helps generate more student interest in the material and enables
the student to learn about both statistical methodology and its application. The 14th
edition contains more than 350 examples and exercises based on real data.
Features and Pedagogy
Authors Anderson, Sweeney, Williams, Camm, Cochran, Fry, and Ohlmann have continued many
of the features that appeared in previous editions. Important ones for students are noted here.
Methods Exercises and Applications Exercises
The end-of-section exercises are split into two parts, Methods and Applications. The Methods exercises require students to use the formulas and make the necessary computations. The
Applications exercises require students to use the chapter material in real-world situations.
Thus, students first ­focus on the computational “nuts and bolts” and then move on to the
subtleties of statistical application and interpretation.
Margin Annotations and Notes and Comments
Margin annotations that highlight key points and provide additional insights for the student are a
key feature of this text. These annotations, which appear in the margins, are designed to provide
emphasis and enhance understanding of the terms and concepts being presented in the text.
At the end of many sections, we provide Notes and Comments designed to give the
student ­additional insights about the statistical methodology and its application. Notes and
Comments ­include warnings about or limitations of the methodology, recommendations for
application, brief descriptions of additional technical considerations, and other matters.
Data Files Accompany the Text
Over 200 data files accompany this text. Data files are provided in Excel format and stepby-step instructions on how to open Excel files in JMP are provided in Appendix 1.1. Files
for use with R are provided in comma-separated-value (CSV) format for easy loading into
the R environment. Step-by-step instructions for importing CSV files into R are provided in
MindTap Reader Appendix R 1.2.
The data files can be accessed from WebAssign within the resources section, ­directly
within the MindTap Reader by clicking on the DATAfile icon, or online directly at
www.cengage.com/decisionsciences/anderson/sbe/14e.
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
xxvii
Preface
Acknowledgments
We would like to acknowledge the work of our reviewers, who provided comments and suggestions of ways to continue to improve our text. Thanks to
AbouEl-Makarim Aboueissa,
University of Southern Maine
Kathleen Arano
Fort Hays State University
Musa Ayar
Uw-baraboo/Sauk County
Kathleen Burke
SUNY Cortland
YC Chang
University of Notre
Dame
David Chen
Rosemont College and
Saint Joseph’s University
Reidar Hagtvedt
University of Alberta
School of Business
Clifford B. Hawley
West Virginia University
Vance A. Hughey
Western Nevada College
Tony Hunnicutt
Ouachita Technical College
Stacey M. Jones
Albers School of Business
and Economics, Seattle
University
Claudiney Pereira
Tulane University
J. G. Pitt
University of Toronto
Scott A. Redenius
Brandeis University
Sandra Robertson
Thomas Nelson
Community College
Sunil Sapra
California State University,
Los Angeles
Dukpa Kim
University of Virginia
Kyle Vann Scott
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of Louisiana
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We continue to owe debt to our many colleagues and friends for their helpful c­ omments
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xxviii
Preface
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Berkeley
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We thank our associates from business and industry who supplied the Statistics in P
­ ractice
features. We recognize them individually by a credit line in each of the articles. We are also
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Foltz; our content manager, Conor Allen; our project manager at MPS Limited, Manoj
­Kumar; and others at Cengage for their editorial counsel and support during the prepartion
of this text.
David R. Anderson
Dennis J. Sweeney
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Chapter 1
Data and Statistics
CONTENTS
STATISTICS IN PRACTICE:
Bloomberg bUSINESSWEEK
1.1 APPLICATIONS IN BUSINESS AND ECONOMICS
Accounting
Finance
Marketing
Production
Economics
Information Systems
1.2 DATA
Elements, Variables, and Observations
Scales of Measurement
Categorical and Quantitative Data
Cross-Sectional and Time Series Data
1.3 DATA SOURCES
Existing Sources
Observational Study
Experiment
Time and Cost Issues
Data Acquisition Errors
1.4 DESCRIPTIVE STATISTICS
1.5 STATISTICAL INFERENCE
1.6 ANALYTICS
1.7 BIG DATA AND DATA MINING
1.8 COMPUTERS AND STATISTICAL ANALYSIS
1.9 ETHICAL GUIDELINES FOR STATISTICAL PRACTICE
Summary 21
Glossary 21
Supplementary Exercises  22
Appendix 1.1 Opening and Saving DATA Files and
Converting to Stacked Form with JMP
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2
Chapter 1
S TAT I S T I C S
I N
Data and Statistics
P R A C T I C E
Bloomberg Businessweek*
NEW YORK, NEW YORK
Bloomberg Businessweek is one of the most widely read
business magazines in the world. Along with feature
articles on current topics, the magazine contains articles
on international business, economic analysis, information
processing, and science and technology. Information in
the feature articles and the regular sections helps readers
stay abreast of current developments and assess the impact of those developments on business and economic
conditions.
Most issues of Bloomberg Businessweek provide an
in-depth report on a topic of current interest. Often, the
in-depth reports contain statistical facts and summaries
that help the reader understand the business and economic information. Examples of articles and reports include the impact of businesses moving important work
to cloud computing, the crisis facing the U.S. Postal
Service, and why the debt crisis is even worse than we
think. In addition, Bloomberg Businessweek provides a
variety of statistics about the state of the economy, including production indexes, stock prices, mutual funds,
and interest rates.
Bloomberg Businessweek also uses statistics and
statistical information in managing its own business.
For example, an annual survey of subscribers helps
the company learn about subscriber demographics,
reading habits, likely purchases, lifestyles, and so on.
Bloomberg Businessweek managers use statistical
summaries from the survey to provide better services
to subscribers and advertisers. One North American
subscriber survey indicated that 64% of Bloomberg
Businessweek subscribers are involved with computer
purchases at work. Such statistics alert Bloomberg
Bloomberg Businessweek uses statistical facts and summaries
in many of its articles. AP Images/Weng lei-Imaginechina
Businessweek managers to subscriber interest in articles
about new developments in computers. The results
of the subscriber survey are also made available to
potential advertisers. The high percentage of subscribers involved with computer purchases at work would be
an incentive for a computer manufacturer to consider
advertising in Bloomberg Businessweek.
In this chapter, we discuss the types of data available
for statistical analysis and describe how the data are obtained. We introduce descriptive statistics and statistical
inference as ways of converting data into meaningful
and easily interpreted statistical information.
*The authors are indebted to Charlene Trentham, Research Manager,
for providing the context for this Statistics in Practice.
Frequently, we see the following types of statements in newspapers and magazines:
●●
●●
●●
●●
Unemployment dropped to an 18-year low of 3.8% in May 2018 from 3.9% in
April and after holding at 4.1% for the prior six months (Wall Street Journal,
June 1, 2018).
Tesla ended 2017 with around $5.4 billion of liquidity. Analysts forecast it
will burn through $2.8 billion of cash this year (Bloomberg Businessweek,
April 19, 2018).
The biggest banks in America reported a good set of earnings for the first three
months of 2018. Bank of America and Morgan Stanley made quarterly net profits of
$6.9 billion and $2.7 billion, respectively (The Economist, April 21, 2018).
According to a study from the Pew Research Center, 15% of U.S. adults say they
have used online dating sites or mobile apps (Wall Street Journal, May 2, 2018).
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1.1 Applications in Business and Economics
●●
3
According to the U.S. Centers for Disease Control and Prevention, in the United
States alone, at least 2 million illnesses and 23,000 deaths can be attributed each year
to antibiotic-resistant bacteria (Wall Street Journal, February 13, 2018).
The numerical facts in the preceding statements—3.8%, 3.9%, 4.1%, $5.4 billion, $2.8
billion $6.9 billion, $2.7 billion, 15%, 2 million, 23,000—are called statistics. In this
usage, the term statistics refers to numerical facts such as averages, medians, percentages,
and maximums that help us understand a variety of business and economic situations.
However, as you will see, the subject of statistics involves much more than numerical facts.
In a broader sense, statistics is the art and science of collecting, analyzing, presenting,
and interpreting data. Particularly in business and economics, the information provided by
collecting, analyzing, presenting, and interpreting data gives managers and decision makers
a better understanding of the business and economic environment and thus enables them to
make more informed and better decisions. In this text, we emphasize the use of statistics
for business and economic decision making.
Chapter 1 begins with some illustrations of the applications of statistics in business
and economics. In Section 1.2 we define the term data and introduce the concept of a data
set. This section also introduces key terms such as variables and observations, discusses
the difference between quantitative and categorical data, and illustrates the uses of cross-­
sectional and time series data. Section 1.3 discusses how data can be obtained from
existing sources or through survey and experimental studies designed to obtain new data.
The uses of data in developing descriptive statistics and in making statistical inferences are
described in Sections 1.4 and 1.5. The last four sections of Chapter 1 provide an introduction to business analytics and the role statistics plays in it, an introduction to big data and
data mining, the role of the computer in statistical analysis, and a discussion of ethical
guidelines for statistical practice.
1.1 Applications in Business and Economics
In today’s global business and economic environment, anyone can access vast amounts of
statistical information. The most successful managers and decision makers understand the
information and know how to use it effectively. In this section, we provide examples that
illustrate some of the uses of statistics in business and economics.
Accounting
Public accounting firms use statistical sampling procedures when conducting audits for
their clients. For instance, suppose an accounting firm wants to determine whether the
amount of accounts receivable shown on a client’s balance sheet fairly represents the
actual amount of accounts receivable. Usually the large number of individual accounts
receivable makes reviewing and validating every account too time-consuming and expensive. As common practice in such situations, the audit staff selects a subset of the accounts
called a sample. After reviewing the accuracy of the sampled accounts, the auditors draw
a conclusion as to whether the accounts receivable amount shown on the client’s balance
sheet is acceptable.
Finance
Financial analysts use a variety of statistical information to guide their investment
recommendations. In the case of stocks, analysts review financial data such as price/
earnings ratios and dividend yields. By comparing the information for an individual
stock with information about the stock market averages, an analyst can begin to draw
a conclusion as to whether the stock is a good investment. For example, the average
dividend yield for the S&P 500 companies for 2017 was 1.88%. Over the same period,
the average dividend yield for Microsoft was 1.72% (Yahoo Finance). In this case, the
statistical information on dividend yield indicates a lower dividend yield for Microsoft
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4
Chapter 1
Data and Statistics
than the average dividend yield for the S&P 500 companies. This and other information
about Microsoft would help the analyst make an informed buy, sell, or hold recommendation for Microsoft stock.
Marketing
Electronic scanners at retail checkout counters collect data for a variety of marketing
research applications. For example, data suppliers such as The Nielsen Company and
IRI purchase point-of-sale scanner data from grocery stores, process the data, and then
sell statistical summaries of the data to manufacturers. Manufacturers spend hundreds of
thousands of dollars per product category to obtain this type of scanner data. Manufacturers also purchase data and statistical summaries on promotional activities such as special
pricing and the use of in-store displays. Brand managers can review the scanner statistics
and the promotional activity statistics to gain a better understanding of the relationship
between promotional activities and sales. Such analyses often prove helpful in establishing
future marketing strategies for the various products.
Production
Today’s emphasis on quality makes quality control an important application of statistics in
production. A variety of statistical quality control charts are used to monitor the output of
a production process. In particular, an x-bar chart can be used to monitor the average output. Suppose, for example, that a machine fills containers with 12 ounces of a soft drink.
Periodically, a production worker selects a sample of containers and computes the average
number of ounces in the sample. This average, or x-bar value, is plotted on an x-bar chart.
A plotted value above the chart’s upper control limit indicates overfilling, and a plotted
value below the chart’s lower control limit indicates underfilling. The process is termed “in
control” and allowed to continue as long as the plotted x-bar values fall between the chart’s
upper and lower control limits. Properly interpreted, an x-bar chart can help determine
when adjustments are necessary to correct a production process.
Economics
Economists frequently provide forecasts about the future of the economy or some aspect
of it. They use a variety of statistical information in making such forecasts. For instance,
in forecasting inflation rates, economists use statistical information on such indicators as
the Producer Price Index, the unemployment rate, and manufacturing capacity utilization.
Often these statistical indicators are entered into computerized forecasting models that
predict inflation rates.
Information Systems
Information systems administrators are responsible for the day-to-day operation of an
organization’s computer networks. A variety of statistical information helps administrators assess the performance of computer networks, including local area networks (LANs),
wide area networks (WANs), network segments, intranets, and other data communication
systems. Statistics such as the mean number of users on the system, the proportion of time
any component of the system is down, and the proportion of bandwidth utilized at various
times of the day are examples of statistical information that help the system administrator
better understand and manage the computer network.
Applications of statistics such as those described in this section are an integral part of
this text. Such examples provide an overview of the breadth of statistical applications. To
supplement these examples, practitioners in the fields of business and economics provided
chapter-opening Statistics in Practice articles that introduce the material covered in each
chapter. The Statistics in Practice applications show the importance of statistics in a wide
variety of business and economic situations.
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1.2 Data
5
1.2 Data
Data are the facts and figures collected, analyzed, and summarized for presentation and
interpretation. All the data collected in a particular study are referred to as the data set for
the study. Table 1.1 shows a data set containing information for 60 nations that participate
in the World Trade Organization. The World Trade Organization encourages the free flow
of international trade and provides a forum for resolving trade disputes.
Elements, Variables, and Observations
Elements are the entities on which data are collected. Each nation listed in Table 1.1 is an
element with the nation or element name shown in the first column. With 60 nations, the
data set contains 60 elements.
A variable is a characteristic of interest for the elements. The data set in Table 1.1
includes the following five variables:
●●
●●
●●
●●
WTO Status: The nation’s membership status in the World Trade Organization; this
can be either as a member or an observer.
Per Capita Gross Domestic Product (GDP) ($): The total market value ($) of all
goods and services produced by the nation divided by the number of people in the
nation; this is commonly used to compare economic productivity of the nations.
Fitch Rating: The nation’s sovereign credit rating as appraised by the Fitch Group1;
the credit ratings range from a high of AAA to a low of F and can be modified by
+ or −.
Fitch Outlook: An indication of the direction the credit rating is likely to move over
the upcoming two years; the outlook can be negative, stable, or positive.
Measurements collected on each variable for every element in a study provide the data.
The set of measurements obtained for a particular element is called an observation. Referring to Table 1.1, we see that the first observation (Armenia) contains the following measurements: Member, 3615, BB-, and Stable. The second observation (Australia) contains
the following measurements: Member, 49755, AAA, and Stable and so on. A data set with
60 elements contains 60 observations.
Scales of Measurement
Data collection requires one of the following scales of measurement: nominal, ordinal,
interval, or ratio. The scale of measurement determines the amount of information contained in the data and indicates the most appropriate data summarization and statistical
analyses.
When the data for a variable consist of labels or names used to identify an attribute
of the element, the scale of measurement is considered a nominal scale. For example,
referring to the data in Table 1.1, the scale of measurement for the WTO Status variable is
nominal because the data “member” and “observer” are labels used to identify the status
category for the nation. In cases where the scale of measurement is nominal, a numerical
code as well as a nonnumerical label may be used. For example, to facilitate data collection and to prepare the data for entry into a computer database, we might use a numerical
code for the WTO Status variable by letting 1 denote a member nation in the World Trade
Organization and 2 denote an observer nation. The scale of measurement is nominal even
though the data appear as numerical values.
The scale of measurement for a variable is considered an ordinal scale if the data
exhibit the properties of nominal data and in addition, the order or rank of the data is
meaningful. For example, referring to the data in Table 1.1, the scale of measurement for
The Fitch Group is one of three nationally recognized statistical rating organizations designated by the U.S. Securities
and Exchange Commission. The other two are Standard & Poor’s and Moody’s.
1
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6
Chapter 1
Data and Statistics
TABLE 1.1
Nations
Data Set for 60 Nations in the World Trade Organization
Nation
WTO
Status
Armenia
Australia
Austria
Azerbaijan
Bahrain
Belgium
Brazil
Bulgaria
Canada
Cape Verde
Chile
China
Colombia
Costa Rica
Croatia
Cyprus
Czech Republic
Denmark
Ecuador
Egypt
El Salvador
Estonia
France
Georgia
Germany
Hungary
Iceland
Ireland
Israel
Italy
Japan
Kazakhstan
Kenya
Latvia
Lebanon
Lithuania
Malaysia
Mexico
Peru
Philippines
Poland
Portugal
South Korea
Romania
Russia
Rwanda
Serbia
Singapore
Slovakia
Member
Member
Member
Observer
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Observer
Member
Member
Observer
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Observer
Member
Member
Per Capita
GDP ($)
3,615
49,755
44,758
3,879
22,579
41,271
8,650
7,469
42,349
2,998
13,793
8,123
5,806
11,825
12,149
23,541
18,484
53,579
6,019
3,478
4,224
17,737
36,857
3,866
42,161
12,820
60,530
64,175
37,181
30,669
38,972
7,715
1,455
14,071
8,257
14,913
9,508
8,209
6,049
2,951
12,414
19,872
27,539
9,523
8,748
703
5,426
52,962
16,530
Fitch
Rating
Fitch
Outlook
BB2
AAA
AAA
BBB2
BBB
AA
BBB
BBB2
AAA
B1
A1
A1
BBB2
BB+
BBB2
B
A1
AAA
B2
B
BB
A1
AAA
BB2
AAA
BB1
BBB
BBB1
A
A2
A1
BBB1
B1
BBB
B
BBB
A2
BBB
BBB
BB1
A2
BB1
AA2
BBB2
BBB
B
BB2
AAA
A1
Stable
Stable
Stable
Stable
Stable
Stable
Stable
Stable
Stable
Stable
Stable
Stable
Stable
Stable
Negative
Negative
Stable
Stable
Positive
Negative
Negative
Stable
Negative
Stable
Stable
Stable
Stable
Stable
Stable
Negative
Negative
Stable
Stable
Positive
Stable
Stable
Stable
Stable
Stable
Stable
Positive
Negative
Stable
Stable
Stable
Stable
Negative
Stable
Stable
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7
1.2 Data
Slovenia
South Africa
Spain
Sweden
Switzerland
Thailand
Turkey
United Kingdom
Uruguay
United States
Zambia
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
Member
21,650
5,275
26,617
51,845
79,888
5,911
10,863
40,412
15,221
57,638
1,270
A2
BBB
A2
AAA
AAA
BBB
BBB2
AAA
BB1
AAA
B1
Negative
Stable
Stable
Stable
Stable
Stable
Stable
Negative
Positive
Stable
Negative
the Fitch Rating is ordinal because the rating labels, which range from AAA to F, can be
rank ordered from best credit rating (AAA) to poorest credit rating (F). The rating letters
provide the labels similar to nominal data, but in addition, the data can also be ranked or
ordered based on the credit rating, which makes the measurement scale ordinal. Ordinal
data can also be recorded by a numerical code, for example, your class rank in school.
The scale of measurement for a variable is an interval scale if the data have all the
properties of ordinal data and the interval between values is expressed in terms of a fixed
unit of measure. Interval data are always numerical. College admission SAT scores are
an example of interval-scaled data. For example, three students with SAT math scores
of 620, 550, and 470 can be ranked or ordered in terms of best performance to poorest
performance in math. In addition, the differences between the scores are meaningful. For
instance, student 1 scored 620 − 550 = 70 points more than student 2, while student 2
scored 550 − 470 = 80 points more than student 3.
The scale of measurement for a variable is a ratio scale if the data have all the properties
of interval data and the ratio of two values is meaningful. Variables such as distance, height,
weight, and time use the ratio scale of measurement. This scale requires that a zero value be
included to indicate that nothing exists for the variable at the zero point. For example, consider the cost of an automobile. A zero value for the cost would indicate that the automobile
has no cost and is free. In addition, if we compare the cost of $30,000 for one automobile to
the cost of $15,000 for a second automobile, the ratio property shows that the first automobile is $30,000/$15,000 = 2 times, or twice, the cost of the second automobile.
Categorical and Quantitative Data
The statistical method
appropriate for summarizing
data depends upon whether
the data are categorical or
quantitative.
Data can be classified as either categorical or quantitative. Data that can be grouped by specific categories are referred to as categorical data. Categorical data use either the nominal
or ordinal scale of measurement. Data that use numeric values to indicate how much or
how many are referred to as quantitative data. Quantitative data are obtained using either
the interval or ratio scale of measurement.
A categorical variable is a variable with categorical data, and a quantitative variable is
a variable with quantitative data. The statistical analysis appropriate for a particular variable
depends upon whether the variable is categorical or quantitative. If the variable is categorical,
the statistical analysis is limited. We can summarize categorical data by counting the number of observations in each category or by computing the proportion of the observations in
each category. However, even when the categorical data are identified by a numerical code,
arithmetic operations such as addition, subtraction, multiplication, and division do not provide
meaningful results. Section 2.1 discusses ways of summarizing categorical data.
Arithmetic operations provide meaningful results for quantitative variables. For
example, quantitative data may be added and then divided by the number of observations
to compute the average value. This average is usually meaningful and easily interpreted. In
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8
Chapter 1
Data and Statistics
general, more alternatives for statistical analysis are possible when data are quantitative.
Section 2.2 and Chapter 3 provide ways of summarizing quantitative data.
Cross-Sectional and Time Series Data
For purposes of statistical analysis, distinguishing between cross-sectional data and time
series data is important. Cross-sectional data are data collected at the same or approximately the same point in time. The data in Table 1.1 are cross-sectional because they
describe the five variables for the 60 World Trade Organization nations at the same point
in time. Time series data are data collected over several time periods. For example, the
time series in Figure 1.1 shows the U.S. average price per gallon of conventional regular
gasoline between 2012 and 2018. From January 2012 until June 2014, prices fluctuated between $3.19 and $3.84 per gallon before a long stretch of decreasing prices from July 2014
to January 2015. The lowest average price per gallon occurred in January 2016 ($1.68).
Since then, the average price appears to be on a gradual increasing trend.
Graphs of time series data are frequently found in business and economic publications.
Such graphs help analysts understand what happened in the past, identify any trends over
time, and project future values for the time series. The graphs of time series data can take
on a variety of forms, as shown in Figure 1.2. With a little study, these graphs are usually
easy to understand and interpret. For example, Panel (A) in Figure 1.2 is a graph that shows
the Dow Jones Industrial Average Index from 2008 to 2018. Poor economic conditions
caused a serious drop in the index during 2008 with the low point occurring in February
2009 (7062). After that, the index has been on a remarkable nine-year increase, reaching its
peak (26,149) in January 2018.
The graph in Panel (B) shows the net income of McDonald’s Inc. from 2008 to 2017. The
declining economic conditions in 2008 and 2009 were actually beneficial to McDonald’s as
the company’s net income rose to all-time highs. The growth in McDonald’s net income
showed that the company was thriving during the economic downturn as people were
cutting back on the more expensive sit-down restaurants and seeking less-expensive
alternatives offered by McDonald’s. McDonald’s net income continued to new all-time
highs in 2010 and 2011, decreased slightly in 2012, and peaked in 2013. After three years of
relatively lower net income, their net income increased to $5.19 billion in 2017.
Panel (C) shows the time series for the occupancy rate of hotels in South Florida over
a one-year period. The highest occupancy rates, 95% and 98%, occur during the months
FIGURE 1.1
U.S. Average Price per Gallon for Conventional Regular Gasoline
$4.50
Average Price per Gallon
$4.00
$3.50
$3.00
$2.50
$2.00
$1.50
$1.00
$0.50
$0.00
Jan-12 Jul-12 Jan-13 Jul-13 Jan-14 Jul-14 Jan-15 Jul-15 Jan-16 Jul-16 Jan-17 Jul-17 Jan-18
Date
Source: Energy Information Administration, U.S. Department of Energy.
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9
1.2 Data
A Variety of Graphs of Time Series Data
30000
25000
20000
15000
10000
5000
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n16
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n15
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n14
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Ja
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0
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n08
Dow Jones Industrial Average Index
Figure 1.2
Date
(A) Dow Jones Industrial Average Index
6
Net Income ($ billions)
5
4
3
2
1
0
2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
Year
(B) Net Income for McDonald’s Inc.
Percentage Occupied
100
80
60
40
20
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ay
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A
ar
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b
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Ja
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0
Month
(C) Occupancy Rate of South Florida Hotels
Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-203
Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience….