Questions to Answer ~ Book Provided!

Answer the questions ~ use graphs, images & excel to show the answer. Please write a good amount for the questions and SHOW WORK!

Page 25 – questions 2, 3, 4

Page 26 – 1.1 1.2 Answer questions from the tables and information regarding the tables from that page

• Part B distinctive about this sample starts with frequency, decimal then relative
• (7) airlines and the questions
• Page 52/53 = Look at histograms and skewness

Page 60 = do numbers 11, 17 & 21

iStockPhoto.com/alongkot-s
Essentials of Modern
Business Statistics
8e
with Microsoft® Excel®
David R. Anderson
University of Cincinnati
Dennis J. Sweeney
University of Cincinnati
Thomas A. Williams
Rochester Institute
of Technology
Jeffrey D. Camm
Wake Forest University
James J. Cochran
The University of Alabama
Michael J. Fry
University of Cincinnati
Jeffrey W. Ohlmann
University of Iowa
Australia ● Brazil ● Mexico ● Singapore ● United Kingdom ● United States
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Essentials of Modern Business Statistics with
Microsoft Excel , 8e
®
®
David R. Anderson, Dennis J. Sweeney,
Thomas A. Williams, Jeffrey D. Camm,
James J. Cochran, Michael J. Fry,
Jeffrey W. Ohlmann
Senior Vice President, Higher Education & Skills
© 2020, 2018 Cengage Learning, Inc.
Unless otherwise noted, all content is © Cengage.
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Printed in the United States of America
Print Number: 01    Print Year: 2019
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Brief Contents
PREFACE xix
ABOUT THE AUTHORS 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
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
Data and Statistics 1
Descriptive Statistics: Tabular and Graphical Displays 35
Descriptive Statistics: Numerical Measures 103
Introduction to Probability 171
Discrete Probability Distributions 217
Continuous Probability Distributions 273
Sampling and Sampling Distributions 305
Interval Estimation 355
Hypothesis Tests 397
Inference About Means and Proportions with Two
Populations 445
Inferences About Population Variances 489
Tests of Goodness of Fit, Independence, and Multiple
Proportions 517
Experimental Design and Analysis of Variance 551
Simple Linear Regression 605
Multiple Regression 685
References and Bibliography 734
Tables 736
Summation Notation 747
Answers to Even-Numbered Exercises (MindTap Reader)
Microsoft Excel and Tools for Statistical Analysis 749
Microsoft Excel Online and Tools for Statistical Analysis 757
Index
765
Chapter 11
Chapter 12
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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).
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Contents
PREFACE xix
ABOUT THE AUTHORS 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 Statistical Analysis Using Microsoft Excel 16
Data Sets and Excel Worksheets 17
Using Excel for Statistical Analysis 18
1.7 Analytics 20
1.8 Big Data and Data Mining 21
1.9 Ethical Guidelines for Statistical Practice 22
Summary 24
Glossary 24
Supplementary Exercises 25
Appendix 1.1 Getting Started with R and RStudio (MindTap Reader)
Appendix 1.2 Basic Data Manipulation in R (MindTap Reader)
Chapter 1
Descriptive Statistics: Tabular and Graphical
Displays  35
Statistics in Practice: Colgate-Palmolive Company 36
2.1 Summarizing Data for a Categorical Variable 37
Frequency Distribution 37
Relative Frequency and Percent Frequency Distributions 38
Chapter 2
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vi
Contents
Using Excel to Construct a Frequency Distribution, a Relative
Frequency Distribution, and a Percent Frequency Distribution 39
Bar Charts and Pie Charts 40
Using Excel to Construct a Bar Chart 42
2.2 Summarizing Data for a Quantitative Variable 47
Frequency Distribution 47
Relative Frequency and Percent Frequency Distributions 49
Using Excel to Construct a Frequency Distribution 50
Dot Plot 51
Histogram 52
Using Excel’s Recommended Charts Tool to Construct
a Histogram 54
Cumulative Distributions 55
Stem-and-Leaf Display 56
2.3 Summarizing Data for Two Variables Using Tables 65
Crosstabulation 65
Using Excel’s PivotTable Tool to Construct a Crosstabulation 68
Simpson’s Paradox 69
2.4 Summarizing Data for Two Variables Using Graphical Displays 75
Scatter Diagram and Trendline 76
Using Excel to Construct a Scatter Diagram and a Trendline 77
Side-by-Side and Stacked Bar Charts 79
Using Excel’s Recommended Charts Tool to Construct
Side-by-Side and Stacked Bar Charts 81
2.5  Data Visualization: Best Practices in Creating Effective Graphical
Displays 85
Creating Effective Graphical Displays 85
Choosing the Type of Graphical Display 86
Data Dashboards 86
Data Visualization in Practice: Cincinnati Zoo
and Botanical Garden 88
Summary 90
Glossary 91
Key Formulas 92
Supplementary Exercises 93
Case Problem 1: Pelican Stores 98
Case Problem 2: Movie Theater Releases 99
Case Problem 3: Queen City 100
Case Problem 4: Cut-Rate Machining, Inc. 100
Appendix 2.1 Creating Tabular and Graphical Presentations with R
(MindTap Reader)
Descriptive Statistics: Numerical Measures   103
Statistics in Practice: Small Fry Design 104
3.1 Measures of Location 105
Mean 105
Chapter 3
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Contents
Median 107
Mode 108
Using Excel to Compute the Mean, Median, and Mode 109
Weighted Mean 109
Geometric Mean 111
Using Excel to Compute the Geometric Mean 112
Percentiles 113
Quartiles 114
Using Excel to Compute Percentiles and Quartiles 115
3.2 Measures of Variability 121
Range 122
Interquartile Range 122
Variance 122
Standard Deviation 124
Using Excel to Compute the Sample Variance and Sample
Standard Deviation 125
Coefficient of Variation 126
Using Excel’s Descriptive Statistics Tool 126
3.3  Measures of Distribution Shape, Relative Location,
and Detecting Outliers 130
Distribution Shape 130
z-Scores 131
Chebyshev’s Theorem 132
Empirical Rule 133
Detecting Outliers 134
3.4 Five-Number Summaries and Boxplots 138
Five-Number Summary 138
Boxplot 138
Using Excel to Construct a Boxplot 139
Comparative Analysis Using Boxplots 139
Using Excel to Construct a Comparative Analysis
Using Boxplots 140
3.5 Measures of Association Between Two Variables 144
Covariance 144
Interpretation of the Covariance 146
Correlation Coefficient 148
Interpretation of the Correlation Coefficient 149
Using Excel to Compute the Sample Covariance
and Sample Correlation Coefficient 151
3.6  Data Dashboards: Adding Numerical Measures to Improve
Effectiveness 153
Summary 156
Glossary 157
Key Formulas 158
Supplementary Exercises 159
Case Problem 1: Pelican Stores 165
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vii
viii
Contents
Case Problem 2: Movie Theater Releases 166
Case Problem 3: Business Schools of Asia-Pacific 167
Case Problem 4: Heavenly Chocolates Website Transactions 167
Case Problem 5: African Elephant Populations 169
Appendix 3.1 Descriptive Statistics with R (MindTap Reader)
Chapter 4
Introduction to Probability   171
Statistics in Practice: National Aeronautics and Space Administration 172
4.1 Experiments, Counting Rules, and Assigning Probabilities 173
Counting Rules, Combinations, and Permutations 174
Assigning Probabilities 178
Probabilities for the KP&L Project 179
4.2 Events and Their Probabilities 183
4.3 Some Basic Relationships of Probability 187
Complement of an Event 187
Addition Law 188
4.4 Conditional Probability 193
Independent Events 196
Multiplication Law 196
4.5 Bayes’ Theorem 201
Tabular Approach 204
Summary 206
Glossary 207
Key Formulas 208
Supplementary Exercises 208
Case Problem 1: Hamilton County Judges 213
Case Problem 2: Rob’s Market 215
Chapter 5
Discrete Probability Distributions   217
Statistics in Practice: Voter Waiting Times in Elections 218
5.1 Random Variables 218
Discrete Random Variables 219
Continuous Random Variables 220
5.2 Developing Discrete Probability Distributions 221
5.3 Expected Value and Variance 226
Expected Value 226
Variance 227
Using Excel to Compute the Expected Value, Variance,
and Standard Deviation 228
5.4  Bivariate Distributions, Covariance, and Financial Portfolios 233
A Bivariate Empirical Discrete Probability Distribution 233
Financial Applications 236
Summary 239
5.5 Binomial Probability Distribution 242
A Binomial Experiment 242
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Contents
Martin Clothing Store Problem 244
Using Excel to Compute Binomial Probabilities 248
Expected Value and Variance for the Binomial
Distribution 249
5.6 Poisson Probability Distribution 252
An Example Involving Time Intervals 253
An Example Involving Length or Distance Intervals 254
Using Excel to Compute Poisson Probabilities 254
5.7 Hypergeometric Probability Distribution 257
Using Excel to Compute Hypergeometric Probabilities 259
Summary 261
Glossary 262
Key Formulas 263
Supplementary Exercises 264
Case Problem 1: Go Bananas! Breakfast Cereal 268
Case Problem 2: McNeil’s Auto Mall 269
Case Problem 3: Grievance Committee at Tuglar Corporation 270
Case Problem 4: Sagittarius Casino 270
Appendix 5.1 Discrete Probability Distributions with R (MindTap Reader)
Continuous Probability Distributions   273
Statistics in Practice: Procter & Gamble 274
6.1  Uniform Probability Distribution 275
Area as a Measure of Probability 276
6.2  Normal Probability Distribution 279
Normal Curve 279
Standard Normal Probability Distribution 281
Computing Probabilities for Any Normal Probability
Distribution 285
Grear Tire Company Problem 286
Using Excel to Compute Normal Probabilities 288
6.3  Exponential Probability Distribution 293
Computing Probabilities for the Exponential Distribution 294
Relationship Between the Poisson
and Exponential Distributions 295
Using Excel to Compute Exponential Probabilities 295
Summary 298
Glossary 298
Key Formulas 298
Supplementary Exercises 299
Case Problem 1: Specialty Toys 301
Case Problem 2: Gebhardt Electronics 302
Appendix 6.1 Continuous Probability Distributions with R
(MindTap Reader)
Chapter 6
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ix
x
Contents
Sampling and Sampling Distributions   305
Statistics in Practice: The Food and Agriculture Organization 306
7.1 The Electronics Associates Sampling Problem 307
7.2 Selecting a Sample 308
Sampling from a Finite Population 308
Sampling from an Infinite Population 312
7.3 Point Estimation 316
Practical Advice 317
7.4 Introduction to Sampling Distributions 319
Chapter 7
7.5  Sampling Distribution of x 322
Expected Value of x 322
Standard Deviation of x 322
Form of the Sampling Distribution of x 324
Sampling Distribution of x for the EAI Problem 324
Practical Value of the Sampling Distribution of x 325
Relationship Between the Sample Size
and the Sampling Distribution of x 327
7.6 Sampling Distribution of p 331
Expected Value of p 332
Standard Deviation of p 332
Form of the Sampling Distribution of p 333
Practical Value of the Sampling Distribution of p 333
7.7 Other Sampling Methods 337
Stratified Random Sampling 337
Cluster Sampling 337
Systematic Sampling 338
Convenience Sampling 338
Judgment Sampling 339
7.8 Practical Advice: Big Data and Errors in Sampling 339
Sampling Error 339
Nonsampling Error 340
Big Data 341
Understanding What Big Data Is 342
Implications of Big Data for Sampling Error 343
Summary 348
Glossary 348
Key Formulas 349
Supplementary Exercises 350
Case Problem: Marion Dairies 353
Appendix 7.1 Random Sampling with R (MindTap Reader)
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Contents
Interval Estimation  355
Statistics in Practice: Food Lion 356
8.1 Population Mean:  Known 357
Margin of Error and the Interval Estimate 357
Using Excel 361
Practical Advice 362
8.2 Population Mean:  Unknown 364
Margin of Error and the Interval Estimate 365
Using Excel 368
Practical Advice 369
Using a Small Sample 369
Summary of Interval Estimation Procedures 371
8.3 Determining the Sample Size 374
8.4 Population Proportion 377
Using Excel 378
Determining the Sample Size 380
8.5 Practical Advice: Big Data and Interval Estimation 384
Big Data and the Precision of Confidence Intervals 384
Implications of Big Data for Confidence Intervals 385
Summary 387
Glossary 388
Key Formulas 388
Supplementary Exercises 389
Case Problem 1: Young Professional Magazine 392
Case Problem 2: GULF Real Estate Properties 393
Case Problem 3: Metropolitan Research, Inc. 395
Appendix 8.1 Interval Estimation with R (MindTap Reader)
Chapter 8
Hypothesis Tests  397
Statistics in Practice: John Morrell & Company 398
9.1 Developing Null and Alternative Hypotheses 399
The Alternative Hypothesis as a Research Hypothesis 399
The Null Hypothesis as an Assumption to Be Challenged 400
Summary of Forms for Null and Alternative Hypotheses 401
9.2 Type I and Type II Errors 402
9.3 Population Mean: s Known 405
One-Tailed Test 405
Two-Tailed Test 410
Using Excel 413
Summary and Practical Advice 414
Relationship Between Interval Estimation
and Hypothesis Testing 415
9.4 Population Mean: s Unknown 420
One-Tailed Test 421
Two-Tailed Test 422
Chapter 9
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xi
xii
Contents
Using Excel 423
Summary and Practical Advice 425
9.5 Population Proportion 428
Using Excel 430
Summary 431
9.6  Practical Advice: Big Data and Hypothesis Testing 434
Big Data, Hypothesis Testing, and p-Values 434
Implications of Big Data in Hypothesis Testing 436
Summary 437
Glossary 438
Key Formulas 438
Supplementary Exercises 439
Case Problem 1: Quality Associates, Inc. 442
Case Problem 2: Ethical Behavior of Business Students at Bayview
University 443
Appendix 9.1 Hypothesis Testing with R (MindTap Reader)
Inference About Means and Proportions with Two
Populations  445
Statistics in Practice: U.S. Food and Drug Administration 446
10.1  Inferences About the Difference Between Two Population Means:
s1 and s2 Known 447
Interval Estimation of m1 2 m2 447
Using Excel to Construct a Confidence Interval 449
Hypothesis Tests About m1 2 m2 451
Using Excel to Conduct a Hypothesis Test 452
Practical Advice 454
10.2  Inferences About the Difference Between
Two Population Means: s1 and s2 Unknown 456
Interval Estimation of m1 2 m2 457
Using Excel to Construct a Confidence Interval 458
Hypothesis Tests About m1 2 m2 460
Using Excel to Conduct a Hypothesis Test 462
Practical Advice 463
10.3  Inferences About the Difference Between Two Population Means:
Matched Samples 467
Using Excel to Conduct a Hypothesis Test 469
10.4  Inferences About the Difference Between
Two Population Proportions 474
Interval Estimation of p1 2 p2 474
Using Excel to Construct a Confidence Interval 476
Hypothesis Tests About p1 2 p2 477
Using Excel to Conduct a Hypothesis Test 479
Summary 483
Glossary 483
Chapter 10
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Contents
xiii
Key Formulas 483
Supplementary Exercises 485
Case Problem: Par, Inc. 488
Appendix 10.1 Inferences About Two Populations with R (MindTap Reader)
Inferences About Population Variances   489
Statistics in Practice: U.S. Government Accountability Office 490
11.1 Inferences About a Population Variance 491
Interval Estimation 491
Using Excel to Construct a Confidence Interval 495
Hypothesis Testing 496
Using Excel to Conduct a Hypothesis Test 498
11.2 Inferences About Two Population Variances 503
Using Excel to Conduct a Hypothesis Test 507
Summary 511
Key Formulas 511
Supplementary Exercises 511
Case Problem 1: Air Force Training Program 513
Case Problem 2: Meticulous Drill & Reamer 514
Appendix 11.1 Population Variances with R (MindTap Reader)
Chapter 11
 ests of Goodness of Fit, Independence, and Multiple
T
Proportions  517
Statistics in Practice: United Way 518
12.1 Goodness of Fit Test 519
Multinomial Probability Distribution 519
Using Excel to Conduct a Goodness of Fit Test 523
12.2 Test of Independence 525
Using Excel to Conduct a Test of Independence 529
12.3  Testing for Equality of Three or More Population Proportions 534
A Multiple Comparison Procedure 537
Using Excel to Conduct a Test of Multiple Proportions 539
Summary 543
Glossary 544
Key Formulas 544
Supplementary Exercises 544
Case Problem 1: A Bipartisan Agenda for Change 547
Case Problem 2: Fuentes Salty Snacks, Inc. 548
Case Problem 3: Fresno Board Games 549
Appendix 12.1 Chi-Square Tests with R (MindTap Reader)
Chapter 12
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xiv
Contents
Experimental Design and Analysis of Variance   551
Statistics in Practice: Burke, Inc. 552
13.1  An Introduction to Experimental Design and Analysis of
Variance 553
Data Collection 554
Assumptions for Analysis of Variance 556
Analysis of Variance: A Conceptual Overview 556
13.2  Analysis of Variance and the Completely Randomized Design 558
Between-Treatments Estimate of Population Variance 559
Within-Treatments Estimate of Population Variance 560
Comparing the Variance Estimates: The F Test 561
ANOVA Table 562
Using Excel 563
Testing for the Equality of k Population Means:
An Observational Study 564
13.3 Multiple Comparison Procedures 570
Fisher’s LSD 570
Type I Error Rates 572
13.4 Randomized Block Design 575
Air Traffic Controller Stress Test 576
ANOVA Procedure 577
Computations and Conclusions 578
Using Excel 579
13.5 Factorial Experiment 584
ANOVA Procedure 585
Computations and Conclusions 586
Using Excel 589
Summary 593
Glossary 594
Key Formulas 595
Completely Randomized Design 595
Multiple Comparison Procedures 596
Randomized Block Design 596
Factorial Experiment 596
Supplementary Exercises 596
Case Problem 1: Wentworth Medical Center 601
Case Problem 2: Compensation for Sales Professionals 602
Case Problem 3: TourisTopia Travel 603
Appendix 13.1 Analysis of Variance with R (MindTap Reader)
Chapter 13
Simple Linear Regression   605
Statistics in Practice: walmart.com 606
14.1 Simple Linear Regression Model 607
Regression Model and Regression Equation 607
Estimated Regression Equation 609
Chapter 14
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Contents
xv
14.2 Least Squares Method 610
Using Excel to Construct a Scatter Diagram, Display
the Estimated Regression Line, and Display the Estimated
Regression Equation 614
14.3 Coefficient of Determination 621
Using Excel to Compute the Coefficient of Determination 625
Correlation Coefficient 626
14.4 Model Assumptions 629
14.5  Testing for Significance 631
Estimate of s2 631
t Test 632
Confidence Interval for b1 633
F Test 634
Some Cautions About the Interpretation of Significance Tests 636
14.6  Using the Estimated Regression Equation for Estimation
and Prediction 639
Interval Estimation 640
Confidence Interval for the Mean Value of y 640
Prediction Interval for an Individual Value of y 641
14.7
Excel’s Regression Tool 646
Using Excel’s Regression Tool for the Armand’s Pizza
Parlors Example 646
Interpretation of Estimated Regression Equation Output 647
Interpretation of ANOVA Output 648
Interpretation of Regression Statistics Output 649
14.8  Residual Analysis: Validating Model Assumptions 651
Residual Plot Against x 652
Residual Plot Against y⁄ 653
Standardized Residuals 655
Using Excel to Construct a Residual Plot 657
Normal Probability Plot 660
14.9 Outliers and Influential Observations 663
Detecting Outliers 663
Detecting Influential Observations 665
14.10  Practical Advice: Big Data and Hypothesis Testing in Simple
Linear Regression 670
Summary 671
Glossary 671
Key Formulas 672
Supplementary Exercises 674
Case Problem 1: Measuring Stock Market Risk 678
Case Problem 2: U.S. Department of Transportation 679
Case Problem 3: Selecting a Point-and-Shoot Digital Camera 680
Case Problem 4: Finding the Best Car Value 681
Case Problem 5: Buckeye Creek Amusement Park 682
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xvi
Contents
Appendix 14.1 Calculus-Based Derivation of Least Squares Formulas 683
Appendix 14.2 A Test for Significance Using Correlation 684
Appendix 14.3 Simple Linear Regression with R (MindTap Reader)
Multiple Regression  685
Statistics in Practice: International Paper 686
15.1  Multiple Regression Model 687
Regression Model and Regression Equation 687
Estimated Multiple Regression Equation 687
15.2  Least Squares Method 688
An Example: Butler Trucking Company 689
Using Excel’s Regression Tool to Develop the Estimated Multiple
Regression Equation 691
Note on Interpretation of Coefficients 693
15.3  Multiple Coefficient of Determination 698
Chapter 15
15.4  Model Assumptions 700
15.5  Testing for Significance 702
F Test 702
t Test 704
Multicollinearity 705
15.6  Using the Estimated Regression Equation for Estimation
and Prediction 708
15.7 Categorical Independent Variables 710
An Example: Johnson Filtration, Inc. 710
Interpreting the Parameters 712
More Complex Categorical Variables 713
15.8  Residual Analysis 718
Residual Plot Against y⁄ 718
Standardized Residual Plot Against y⁄ 719
15.9  Practical Advice: Big Data and Hypothesis
Testing in Multiple Regression 722
Summary 723
Glossary 723
Key Formulas 724
Supplementary Exercises 725
Case Problem 1: Consumer Research, Inc. 729
Case Problem 2: Predicting Winnings for NASCAR Drivers 730
Case Problem 3: Finding the Best Car Value 732
Appendix 15.1 Multiple Linear Regression with R (MindTap Reader)
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xvii
Contents
Appendix A  References and Bibliography 734
Appendix B
Tables 736
Appendix C
Summation Notation 747
Appendix D   Answers to Even-Numbered Exercises (MindTap Reader)
Appendix E   Microsoft Excel and Tools for Statistical Analysis 749
Appendix F  Microsoft Excel Online and Tools for Statistical Analysis 757
Index 765
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Preface
T
his text is the eight edition of Essentials of Modern Business Statistics with Microsoft®
Excel®. With this edition we welcome two eminent scholars to our author team:
Michael J. Fry of the University of Cincinnati and Jeffrey W. Ohlmann of the University of
Iowa. Both Mike and Jeff are accomplished teachers, researchers, and practitioners in the
fields of statistics and business analytics. You can read more about their accomplishments in
the About the Authors section that follows this preface. We believe that the addition of Mike
and Jeff as our coauthors will both maintain and improve the effectiveness of Essentials of
Modern Business Statistics with Microsoft Excel.
The purpose of Essentials of Modern Business Statistics with Microsoft Excel 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 knowledge 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 applications setting, with the statistical results providing insights to
decisions and solutions to applied 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.
Use of Microsoft Excel for Statistical Analysis
Essentials of Modern Business Statistics with Microsoft Excel is first and foremost a statistics textbook that emphasizes statistical concepts and applications. But since most practical
problems are too large to be solved using hand calculations, some type of statistical software
package is required to solve these problems. There are several excellent statistical packages
available today. However, because most students and potential employers value spreadsheet
experience, many schools now use a spreadsheet package in their statistics courses. Microsoft Excel is the most widely used spreadsheet package in business as well as in colleges and
universities. We have written Essentials of Modern Business Statistics with Microsoft Excel
especially for statistics courses in which Microsoft Excel is used as the software package.
Excel has been integrated within each of the chapters and plays an integral part in providing an application orientation. Although we assume that readers using this text are
familiar with Excel basics such as selecting cells, entering formulas, and copying we do
not assume that readers are familiar with Excel or Excel’s tools for statistical analysis. As
a result, we have included Appendix E, which provides an introduction to Excel and tools
for statistical analysis.
Throughout the text the discussion of using Excel to perform a statistical procedure appears in a subsection immediately following the discussion of the statistical procedure. We
believe that this style enables us to fully integrate the use of Excel throughout the text, but
still maintain the primary emphasis on the statistical methodology being discussed. In each
of these subsections, we use a standard format for using Excel for statistical analysis. There
are four primary tasks: Enter/Access Data, Enter Functions and Formulas, Apply Tools, and
Editing Options. We believe a consistent framework for applying Excel helps users to focus
on the statistical methodology without getting bogged down in the details of using Excel.
In presenting worksheet figures we often use a nested approach in which the worksheet
shown in the background of the figure displays the formulas and the worksheet shown in the
foreground shows the values computed using the formulas. Different colors and shades of
colors are used to differentiate worksheet cells containing data, highlight cells containing
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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.
xx
Preface
Excel functions and formulas, and highlight material printed by Excel as a result of using
one or more data analysis tools.
Changes in the Eighth Edition
We appreciate the acceptance and positive response to the previous editions of Essentials of
Modern Business Statistics with Microsoft Excel. Accordingly, in making modifications for
this new edition, we have maintained the presentation style and readability of those editions.
The significant changes in the new edition are summarized here.
●●
●●
●●
●●
Software. In addition to step-by-step instructions and screen captures that show
how to use the latest version of Excel to implement statistical procedures, we also
provide instructions for Excel Online and R through the MindTap Reader.
New Examples and Exercises Based on Real Data. In this edition, we have added
headers to all Applications exercises to make the application of each exercise more
clear. We have also added over 160 new examples and exercises based on real data
and referenced sources. By using data from sources also used by The Wall Street
Journal, USA Today, The Financial Times, Forbes, 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 generates greater
student interest in the material and enables the student to more effectively learn
about both statistical methodology and its application.
Case Problems. We have added four new case problems to this edition. The 47 case
problems in the text provide students with the opportunity to analyze somewhat
larger data sets and prepare managerial reports based on the results of their analysis.
Appendixes for Use of R. We now provide appendixes in the MindTap Reader for
many chapters that demonstrate the use of the popular open-source software R and
RStudio for statistical applications. The use of R is not required to solve any problems or cases in the textbook, but the appendixes provide an introduction to R and
RStudio for interested instructors and students.
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.
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xxi
Preface
Data Files Accompany the Text
Over 250 data files are available on the website that accompanies the text. DATAfile logos
are used in the text to identify the data sets that are available on the website. Data sets for all
case problems as well as data sets for larger exercises are included.
MindTap
MindTap, featuring all new Excel Online integration powered by Microsoft, is a complete
digital solution for the business statistics course. It has enhancements that take students from
learning basic statistical concepts to actively engaging in critical thinking applications, while
learning valuable software skills for their future careers. The R appendixes for many of the
chapters in the text are also accessible through MindTap.
MindTap is a customizable digital course solution that includes an interactive eBook and
autograded, algorithmic exercises from the textbook. All of these materials offer students
better access to understand the materials within the course. For more information on MindTap, please contact your Cengage representative.
For Students
Online resources are available to help the student work more efficiently. The resources can
be accessed at www.cengage.com/decisionsciences/anderson/embs/8e.
For Instructors
Instructor resources are available to adopters on the Instructor Companion Site, which can
be found and accessed at www.cengage.com/decisionsciences/anderson/embs/8e, including:
●●
●●
●●
●●
Solutions Manual: The Solutions Manual, prepared by the authors, includes solutions for all problems in the text. It is available online as well as print.
Solutions to Case Problems: These are also prepared by the authors and contain
solutions to all case problems presented in the text.
PowerPoint Presentation Slides: The presentation slides contain a teaching outline that incorporates figures to complement instructor lectures.
Test Bank: Cengage Learning Testing Powered by Cognero is a flexible, online
system that allows you to:
●●
author, edit, and manage test bank content from multiple Cengage Learning
solutions,
●●
create multiple test versions in an instant, and
●●
deliver tests from your LMS, your classroom, or wherever you want.
Acknowledgments
A special thanks goes to our associates from business and industry who supplied the Statistics in Practice features. We recognize them individually by a credit line in each of the articles. We are also indebted to our senior product manager, Aaron Arnsparger; our content
manager, Conor Allen; senior learning designer, Brandon Foltz; digital delivery lead, Mark
Hopkinson; and our senior project managers at MPS Limited, Santosh Pandey & Manoj
Kumar, for their editorial counsel and support during the preparation of this text.
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:
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xxii
Preface
Jamal Abdul-Hafidh
University of Missouri–St.
Louis
Yvonne Brown
Pima Community
College
Nicolas Farnum
California State University,
Fullerton
Chris Adalikwu
Concordia College
Dawn Bulriss
Maricopa Community
Colleges
Abe Feinberg
California State University,
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Robert Burgess
Georgia Tech
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Woodbury University
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Murray State University
Ardavan Asef-Vaziri
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Von L. Burton
Athens State University
John R. Carpenter
Cornerstone University
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University of Arizona
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Cleveland State
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Louis
Si Chen
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Highline Community
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New York Institute of
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Maryville University
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Texas Christian University
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University of Scranton
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DePauw University
V. Daniel Guide
Duquesne University
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Chennai Business School
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Dominican University
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North Carolina A&T
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University of Houston,
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University of Wisconsin–
River Falls
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University of Memphis
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Northwest Shoals
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Eugene Jones
The Ohio State University
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Buena Vista University
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Wallace Community College
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Francisco
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Eastern Shore
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University
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California State University,
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University
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Louisiana
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Pellissippi State Tech
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xxiv
Preface
Harvey A. Singer
George Mason
University
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Prairie View A&M
University
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Monmouth University
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University of Montana
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We would like to recognize the following individuals who have helped us in the past and
continue to influence our writing.
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of Textiles and Science
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of Technology
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of Technology
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University of Rhode Island
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About the Authors
David R. Anderson. David R. Anderson is Professor Emeritus in the Carl H. Lindner
College of Business 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 in the Carl H. Lindner
College of Business 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 Business 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 Duke Energy 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 Science
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 has taught 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 science,
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
Business 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.
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xxvi
About the Authors
Prior to 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 30 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 the INFORMS Journal on Applied Analytics
(formerly Interfaces).
James J. Cochran. James J. Cochran is Associate Dean for Research, Professor of Applied
Statistics, and the Rogers-Spivey 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 Pôle Universitaire Léonard 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, was
named a Fellow of the American Statistical Association in 2011, and was named a Fellow
of INFORMS in 2017. He also received the Founders Award in 2014 and the Karl E. Peace
Award in 2015 from the American Statistical Association as well as the President’s Award
in 2018 from INFORMS. A strong advocate for effective operations research and statistics
education as a means of improving the quality of applications to real problems, Professor
Cochran has organized and chaired teaching effectiveness workshops in Uruguay, South
Africa, Colombia, India, Argentina, Kenya, Cuba, Croatia, Cameroon, Nepal, Moldova, and
Bulgaria. He has served as a statistical 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 INFORMS Journal of Applied Analytics (formerly Interfaces), International Transactions in Operational Research, and Significance.
Michael J. Fry. Michael J. Fry is Professor of Operations, Business Analytics, and
Information Systems (OBAIS) 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 B.S. 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. He serves on editorial boards for journals such as
Production and Operations Management, INFORMS Journal of Applied Analytics (formerly
Interfaces), Omega, and Journal of Quantitative Analysis in Sports. His research interests
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About the Authors
xxvii
are in applying analytics to the areas of supply chain management, sports, 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. In 2019 he led the team that
was awarded the INFORMS UPS George D. Smith Prize on behalf of the OBAIS Department at the University of Cincinnati.
Jeffrey W. Ohlmann. Jeffrey W. Ohlmann is Associate Professor of Business Analytics
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 M.S.
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 two dozen research papers in journals such as Operations Research,
Mathematics of Operations Research, INFORMS Journal on Computing, Transportation
Science, and European Journal of Operational Research. 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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iStockPhoto.com/alongkot-s
Essentials of Modern
Business Statistics
8e
with Microsoft® Excel®
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Chapter 1
Data and Statistics
CONTENTS
STATISTICS IN PRACTICE:
Bloomberg bUSINESSWEEK
1.1 A
 PPLICATIONS IN BUSINESS AND ECONOMICS
Accounting
Finance
Marketing
Production
Economics
Information Systems
 ATA
1.2 D
Elements, Variables, and Observations
Scales of Measurement
Categorical and Quantitative Data
Cross-Sectional and Time Series Data
1.3 D
 ATA SOURCES
Existing Sources
Observational Study
Experiment
Time and Cost Issues
Data Acquisition Errors
1.4 D
 ESCRIPTIVE STATISTICS
1.5 S
 TATISTICAL INFERENCE
1.6 S
 TATISTICAL ANALYSIS USING MICROSOFT EXCEL
Data Sets and Excel Worksheets
Using Excel for Statistical Analysis
1.7 ANALYTICS
1.8 BIG DATA AND DATA MINING
1.9 E
 THICAL GUIDELINES FOR STATISTICAL PRACTICE
Summary 24
Glossary 24
Supplementary Exercises  25
APPENDIXES
Appendix 1.1: Getting Started with R and RStudio
(MindTap Reader)
Appendix 1.2: Basic Data Manipulation in R
(MindTap Reader)
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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
Bloomberg Businessweek uses statistical facts and summaries
in many of its articles. AP Images/Weng lei-Imaginechina
purchases at work. Such statistics alert Bloomberg
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 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 the role
of the computer in statistical analysis, an introduction to business analytics and the role
statistics plays in it, an introduction to big data and data mining, 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 (WTO). The WTO 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 as 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 1 or 2.
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 contains the following measurements:
Member, 3615, BB–, and Stable. The second observation contains the following
measurements: Member, 49755, AAA, 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 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
1
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 and Poor’s and Moody’s investor service.
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6
Chapter 1
Data and Statistics
TABLE 1.1
Nations
Data sets such as Nations
are available on the companion site for this title.
Data Set for 60 Nations in the World Trade Organization
Nation
WTO
Status
Per Capita
GDP ($)
Fitch
Rating
Fitch
Outlook
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
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
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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1.2
7
Data
Slovenia
South Africa
Spain
Sweden
Switzerland
Thailand
Turkey
United Kingdom
United States
Uruguay
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
57,638
15,221
1,270
A2
BBB
A2
AAA
AAA
BBB
BBB2
AAA
AAA
BB1
B1
Negative
Stable
Stable
Stable
Stable
Stable
Stable
Negative
Stable
Positive
Negative
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 numeric. 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 per­
formance in math. In addition, the differences between the scores are meaningful. For
instance, ­student 1 scored 620 2 550 5 70 points more than student 2, while student 2
scored 550 2 470 5 80 points more than student 3.
The scale of measurement for a variable is a ratio scale if the data have all the prop­
erties 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 5 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 (7,062). 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
$0.00
Jan-12 Jul-12 Jan-13 Jul-13 Jan-14 Jul-14 Jan-15 Jul-15 Jan-16 Jul-16 Jan-17 Jul-17 Jan-18
Date
Source: Energy Information Administration, U.S. Department of Energy.
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
9
Data
A Variety of Graphs of Time Series Data
30,000
25,000
20,000
15,000
10,000
5,000
Ja
n18
Ja
n17
Ja
n16
Ja
n15
Ja
n14
Ja
n13
Ja
n12
Ja
n11
Ja
n10
0
Ja
n08
Dow Jones Industrial Average Index
Figure 1.2
Ja
n09
1.2
Date
(A) Dow Jones Industrial Average Index
6
Net Income ($ 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
ec
D
Ju
l
A
ug
Se
p
O
ct
N
ov
Ju
n
ay
pr
M
A
ar
b
Fe
M
n
Ja
0
Month
(C) Occupancy Rate of South Florida Hotels
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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.
10
Chapter 1
Data and Statistics
of February and March when the climate of South Florida is attractive to tourists. In fact,
January to April of each year is typically the high-occupancy season for South Florida hotels.
On the other hand, note the low occupancy rates during the months of August to October,
with the lowest occupancy rate of 50% occurring in September. High temperatures and the
hurricane season are the primary reasons for the drop in hotel occupancy during this period.
N O T E S
+
C O M M E N T S
1. An observation is the set of measurements obtained for
each element in a data set. Hence, the number of observations is always the same as the number of elements.
The number of measurements obtained for each element
equals the number of variables. Hence, the total number
of data items can be determined by multiplying the number of observations by the number of variables.
2. Quantitative data may be discrete or continuous. Quantitative data that measure how many (e.g., number of calls
received in 5 minutes) are discrete. Quantitative data that
measure how much (e.g., weight or time) are continuous
because no separation occurs between the possible data
values.
1.3 Data Sources
Data can be obtained from existing sources, by conducting an observational study, or by
conducting an experiment.
Existing Sources
In some cases, data needed for a particular application already exist. Companies maintain
a variety of databases about their employees, customers, and business operations. Data
on ­employee salaries, ages, and years of experience can usually be obtained from internal
personnel records. Other internal records contain data on sales, advertising expenditures, distri­bution costs, inventory levels, and production quantities. Most companies also
maintain detailed data about their customers. Table 1.2 shows some of the data commonly
available from internal company records.
Organizations that specialize in collecting and maintaining data make available substantial amounts of business and economic data. Companies access these external data
sources through leasing arrangements or by purchase. Dun & Bradstreet, Bloomberg, and
Dow Jones & Company are three firms that provide extensive business database services
to clients. The Nielsen Company and IRI built successful businesses collecting and processing data that they sell to advertisers and product manufacturers.
TABLE 1.2
Examples of Data Available from Internal Company Records
Source
Some of the Data Typically Available
Employee records
Name, address, social security number, salary, number of vacation
days, number of sick days, and bonus
Production records
Part or product number, quantity produced, direct labor cost, and
materials cost
Inventory records
Part or product number, number of units on hand, reorder level,
economic order quantity, and discount schedule
Sales records
Product number, sales volume, sales volume by region, and sales
volume by customer type
Credit records
Customer name, address, phone number, credit limit, and accounts
receivable balance
Customer profile
Age, gender, income level, household size, address, and preferences
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11
Data Sources
Data are also available from a variety of industry associations and special interest
organizations. The U.S. Travel Association maintains travel-related information such as
the number of tourists and travel expenditures by states. Such data would be of ­interest to
firms and individuals in the travel industry. The Graduate Management ­Admission Council
maintains data on test scores, student characteristics, and graduate management education
programs. Most of the data from these types of sources are available to qualified users at a
modest cost.
The Internet is an important source of data and statistical information. Almost all
companies maintain websites that provide general information about the company as well
as data on sales, number of employees, number of products, product prices, and product
specifications. In addition, a number of companies now specialize in making information
available over the Internet. As a result, one can obtain access to stock quotes, meal prices at
restaurants, salary data, and an almost infinite variety of information.
Government agencies are another important source of existing data. For instance, the
website DATA.GOV was launched by the U.S. government in 2009 to make it easier for the
public to access data collected by the U.S. federal government. The DATA.GOV website
includes over 150,000 data sets from a variety of U.S. federal departments and agencies,
but there are many other federal agencies that maintain their own websites and data repositories. Table 1.3 lists selected governmental agencies and some of the data they provide.
Figure 1.3 shows the home-page for the DATA.GOV website. Many state and local governments are also now providing data sets online. As examples, the states of California and
Texas maintain open data portals at data.ca.gov and data.texas.gov, respectively. New York
City’s open data website is opendata.cityofnewyork.us and the city of Cincinnati, Ohio, is
at data.cincinnati-oh.gov.
Observational Study
In an observational study we simply observe what is happening in a particular situation,
record data on one or more variables of interest, and conduct a statistical analysis of the
resulting data. For example, researchers might observe a randomly selected group of
customers that enter a Walmart supercenter to collect data on variables such as the length
of time the customer spends shopping, the gender of the customer, and the amount spent.
Statistical analysis of the dat…