Contents
Chapter 1
Overview of Statistics 2
1.1 What is Statistics? 3
1.2 Why Study Statistics? 5
1.3 Applying Statistics in Business 7
1.4 Statistical Challenges 10
1.5 Critical Thinking 16
Chapter Summary 19
Chapter Exercises 19
Chapter 2
Data Collection 24
2.1 Variables and Data 25
2.2 Level of Measurement 29
2.3 Sampling Concepts 33
2.4 Sampling Methods 36
2.5 Data Sources 44
2.6 Surveys 46
Chapter Summary 51
Chapter Exercises 51
Chapter 3
Describing Data Visually 56
3.1 Stem-and-Leaf Displays and Dot Plots 57
3.2 Frequency Distributions and Histograms 61
3.3 Effective Excel Charts 69
3.4 Line Charts 71
3.5 Column and Bar Charts 74
3.6 Pie Charts 78
3.7 Scatter Plots 80
3.8 Tables 84
3.9 Deceptive Graphs 87
Chapter Summary 90
Chapter Exercises 91
Chapter 4
Descriptive Statistics 100
4.1 Numerical Description 101
4.2 Measures of Center 103
4.3 Measures of Variability 115
4.4 Standardized Data 123
4.5 Percentiles, Quartiles, and Box Plots 128
4.6 Covariance and Correlation 137
4.7 Grouped Data 141
4.8 Skewness and Kurtosis 143
Chapter Summary 147
Chapter Exercises 149
Chapter 5
Probability 158
5.1 Random Experiments 159
5.2 Probability 161
5.3 Rules of Probability 165
5.4 Independent Events 170
5.5 Contingency Tables 174
5.6 Tree Diagrams 181
5.7 Bayes’ Theorem 183
5.8 Counting Rules 189
Chapter Summary 192
Chapter Exercises 193
Chapter 6
Discrete Probability Distributions 200
6.1 Discrete Probability Distributions 201
6.2 Expected Value and Variance 204
6.3 Uniform Distribution 208
6.4 Binomial Distribution 210
6.5 Poisson Distribution 217
6.6 Hypergeometric Distribution 223
6.7 Geometric Distribution (Optional) 227
6.8 Transformations of Random Variables (Optional) 229
Chapter Summary 232
Chapter Exercises 234
Chapter 7
Continuous Probability Distributions 238
7.1 Continuous Probability Distributions 239
7.2 Uniform Continuous Distribution 241
7.3 Normal Distribution 243
7.4 Standard Normal Distribution 246
7.5 Normal Approximations 259
7.6 Exponential Distribution 263
7.7 Triangular Distribution (Optional) 268
Chapter Summary 271
Chapter Exercises 273
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Contents xxiii
Chapter 8
Sampling Distributions and Estimation 278
8.1 Sampling and Estimation 279
8.2 Central Limit Theorem 283
8.3 Confidence Interval for a Mean (μ) With Known σ 287
8.4 Confidence Interval for a Mean (μ) With Unknown σ 291
8.5 Confidence Interval for a Proportion (π) 297
8.6 Estimating from Finite Populations 304
8.7 Sample Size Determination for a Mean 306
8.8 Sample Size Determination for a Proportion 308
8.9 Confidence Interval for a Population Variance, σ2 (Optional) 311
Chapter Summary 313
Chapter Exercises 315
Chapter 9
One-Sample Hypothesis Tests 322
9.1 Logic of Hypothesis Testing 323
9.2 Type I and Type II Errors 326
9.3 Decision Rules and Critical Values 330
9.4 Testing a Mean: Known Population Variance 333
9.5 Testing a Mean: Unknown Population Variance 340
9.6 Testing a Proportion 345
9.7 Power Curves and OC Curves (Optional) 354
9.8 Tests for One Variance (Optional) 360
Chapter Summary 362
Chapter Exercises 364
Chapter 10
Two-Sample Hypothesis Tests 370
10.1 Two-Sample Tests 371
10.2 Comparing Two Means: Independent Samples 373
10.3 Confidence Interval for the Difference of Two Means, μ1 − μ2 381
10.4 Comparing Two Means: Paired Samples 383
10.5 Comparing Two Proportions 389
10.6 Confidence Interval for the Difference of Two Proportions, π1 − π2 397
10.7 Comparing Two Variances 398
Chapter Summary 405
Chapter Exercises 406
Chapter 11
Analysis of Variance 416
11.1 Overview of ANOVA 417
11.2 One-Factor ANOVA (Completely Randomized Model) 419
11.3 Multiple Comparisons 427
11.4 Tests for Homogeneity Of Variances 429
11.5 Two-Factor ANOVA Without Replication (Randomized Block Model) 433
11.6 Two-Factor ANOVA with Replication (Full Factorial Model) 441
11.7 Higher-Order ANOVA Models (Optional) 449
Chapter Summary 452
Chapter Exercises 453
Chapter 12
Simple Regression 462
12.1 Visual Displays and Correlation Analysis 463
12.2 Simple Regression 469
12.3 Regression Models 471
12.4 Ordinary Least Squares Formulas 475
12.5 Tests for Significance 479
12.6 Analysis of Variance: Overall Fit 485
12.7 Confidence and Prediction Intervals for Y 489
12.8 Residual Tests 492
12.9 Unusual Observations 498
12.10 Other Regression Problems (Optional) 502
12.11 Logistic Regression (Optional) 505
Chapter Summary 507
Chapter Exercises 509
Chapter 13
Multiple Regression 522
13.1 Multiple Regression 523
13.2 Assessing Overall Fit 528
13.3 Predictor Significance 532
13.4 Confidence Intervals for Y 536
13.5 Categorical Variables 538
13.6 Tests for Nonlinearity and Interaction 547
13.7 Multicollinearity 550
13.8 Regression Diagnostics 554
13.9 Other Regression Topics 560
13.10 Logistic Regression (Optional) 562
Chapter Summary 564
Chapter Exercises 566
Chapter 14
Time-Series Analysis 578
14.1 Time-Series Components 579
14.2 Trend Forecasting 583
14.3 Assessing Fit 596
14.4 Moving Averages 598
14.5 Exponential Smoothing 600
14.6 Seasonality 604
14.7 Index Numbers 609
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xxiv Contents
14.8 Forecasting: Final Thoughts 611
Chapter Summary 612
Chapter Exercises 614
Chapter 15
Chi-Square Tests 624
15.1 Chi-Square Test for Independence 625
15.2 Chi-Square Tests for Goodness of Fit 636
15.3 Uniform Goodness-of-Fit Test 639
15.4 Poisson Goodness-of-Fit Test 643
15.5 Normal Chi-Square Goodness-of-Fit Test 648
15.6 ECDF Tests (Optional) 651
Chapter Summary 652
Chapter Exercises 653
Chapter 16
Nonparametric Tests 662
16.1 Why Use Nonparametric Tests? 663
16.2 One-Sample Runs Test 664
16.3 Wilcoxon Signed-Rank Test 667
16.4 Wilcoxon Rank Sum Test 670
16.5 Kruskal-Wallis Test for Independent Samples 673
16.6 Friedman Test for Related Samples 678
16.7 Spearman Rank Correlation Test 681
Chapter Summary 684
Chapter Exercises 685
Chapter 17
Quality Management 692
17.1 Quality and Variation 693
17.2 Pioneers in Quality Management 695
17.3 Quality Improvement 697
17.4 Control Charts: Overview 701
17.5 Control Charts for a Mean 702
17.6 Control Charts for a Range 710
17.7 Other Control Charts 711
17.8 Patterns in Control Charts 716
17.9 Process Capability 718
17.10 Additional Quality Topics (Optional) 721
Chapter Summary 725
Chapter Exercises 726
Chapter 18
Simulation 18-1
Appendixes
A Binomial Probabilities 734
B Poisson Probabilities 736
C-1 Standard Normal Areas 739
C-2 Cumulative Standard Normal Distribution 740
D Student’s t Critical Values 742
E Chi-Square Critical Values 743
F Critical Values of F.10 744
G Solutions to Odd-Numbered Exercises 752
H Answers to Exam Review Questions 779
I Writing and Presenting Reports 781
J Statistics in Excel and R 785
K Using R and RStudio 789
Index 797
Standard Normal Areas 815
Cumulative Standard
Normal Distribution 816
Student’s t Critical Values 818
When managers are well informed about a com-
pany’s internal operations (e.g., sales, production, inventory levels, time to market, warranty claims) and competitive position (e.g., market share, customer satisfaction, repeat sales), they can take appropriate actions to improve their business. Managers need reliable, timely information so they can analyze market trends and adjust to changing market conditions. Better data also can help a company decide which types of strategic information it should share with trusted business partners to improve its supply chain. Statistics and statistical analysis permit databased decision making and reduce managers’ need to rely on guesswork.
Statistics is a key component of the field of business intelligence, which encompasses all the technologies for collecting, storing, accessing, and analyzing data on the company’s operations in order to make better business
decisions. Statistics helps convert unstructured “raw” data (e.g., point-of-sale data, customer spending patterns) into useful information through online analytical processing (OLAP) and data mining, terms that you may have encountered in your other business classes. Statistical analysis focuses attention on key problems and guides discussion toward issues, not personalities or territorial struggles. While powerful database software and query systems are the key to managing a firm’s data warehouse, relatively small Excel spreadsheets are often the focus of discussion among managers when it comes to “bottom line” decisions. That is why Excel is featured prominently in this textbook. In short, companies increasingly are using business analytics to support decision making, to recognize anomalies that require tactical action, or to gain strategic insight to align business processes with business objectives.
Answers to questions such as “How likely is this event?” or “What if this trend continues?” will lead to appropriate actions. Businesses that combine managerial judgment with statistical analysis are more successful.
1.1 WHAT IS STATISTICS?
Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data. Some experts prefer to call statistics data science, a trilogy of tasks involving data modeling, analysis, and decision making. A statistic is a single measure, reported as a number, used LO 1-1
Define statistics and explain some of its uses.
Juice Images/Getty Images
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to summarize a sample data set. Statistics may be thought of as a collection of methodolo-
gies to summarize, draw valid conclusions, and make predictions from empirical measurements. Statistics helps us organize and present information and extract meaning from raw data. Although it is often associated with the sciences and medicine, statistics is now used in every academic field and every area of business.
Plural or Singular?
Statistics The science of collecting, organizing, analyzing, interpreting, and presenting data.
Statistic A single measure, reported as a number, used to summarize a sample data set.
Sampling and Surveys (Ch 2)
Visual Displays (Ch 3)
Numerical Summaries
(Ch 4)
Probability
Models
(Chs 5–8)
Estimating Parameters
(Ch 8)
Testing
Hypotheses
(Chs 9–16)
Regression and Trends
(Chs 12–14)
Quality Control (Ch 17)
Making Inferences from Samples
Collecting and Describing Data Statistics
Figure 1.1
Overview of Statistics
Many different measures can be used to summarize data sets. You will learn throughout this textbook that there can be different measures for different sets of data and different measures for different types of questions about the same data set. Consider, for example, a sample data set that consists of heights of students in a university. There could be many different uses for this data set. Perhaps the manufacturer of graduation gowns wants to know how long to make the gowns; the best statistic for this would be the average height of the students. But an architect designing a classroom building would want to know how high the doorways should be and would base measurements on the maximum height of the students. Both the average and the maximum are examples of a statistic. You may not have a trained statistician in your organization, but any college graduate is expected to know something about statistics, and anyone who creates graphs or interprets data is “doing statistics” without an official title. There are two primary kinds of statistics:
∙ Descriptive statistics refers to the collection, organization, presentation, and summary of data (either using charts and graphs or using a numerical summary).
∙ Inferential statistics refers to generalizing from a sample to a population, estimating unknown population parameters, drawing conclusions, and making decisions. Figure 1.1 identifies the tasks and the text chapters for each.
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1.2 WHY STUDY STATISTICS?
A BusinessWeek article called statistics and probability “core skills for business people” in order to know when others are dissembling, to build financial models, or to develop a marketing plan. The 2019 Job Outlook survey conducted by the National Association of Colleges
LO 1-2
List reasons for a business student to study statistics.
What Is Business Analytics?
Analytics is a broad field that uses statistics, mathematics, and computational tools to extract information from data. Analytics tools fall into three categories: descriptive, predictive, and prescriptive. This terminology derived from the questions we are trying to answer.
What happened? Businesses use descriptive analytics tools to analyze historical data and help them identify trends and patterns. What is likely to happen next? Businesses use predictive analytics tools to predict probabilities of future events and help them forecast consumer behavior.
What actions do we take to achieve our goals?
Businesses use prescriptive analytics tools to help them make decisions on how to achieve objectives within real-world constraints.
Analytics in Action
Using Analytics to Improve Business
Descriptive Analytics: Google Analytics provides a wide range of metrics for companies that want to better understand how their websites operate. This type of descriptive analytics allows companies to see, for example, loading time for their pages in different browsers and on different devices; how much time a viewer spends on the page; and the number of visits per hour, day, or week. In addition, companies can see performance measures such as bounce rate or click-through rate. Bounce rate shows the percentage of viewers who leave the site after viewing only the homepage. Click-through rate is the percentage of viewers who click on the ad when they view it on a webpage. Both of these metrics are important for evaluating the effectiveness of a web design.
Predictive Analytics: In 2015 Oracle acquired Datalogix, a company that analyzes consumer purchasing behavior to help its customers design the most effective digital marketing campaigns. The acquisition of Datalogix strengthened the tools Oracle provides
as part of its data cloud offerings. Predictive analytics has been the key to Datalogix’s success. Dr Pepper is one of its happy customers. When Dr Pepper wanted to increase sales, it turned to Datalogix for help in designing a successful Facebook advertising campaign. Through the use of analytics, Datalogix showed that by targeting Facebook users who purchased carbonated beverages and those who purchased Dr Pepper products in particular, Dr Pepper was able to increase its sales by 1.5 percent. And for every $1 spent on advertising, Dr Pepper saw a $3 increase in revenue. (www.datalogix.com)
Prescriptive Analytics: Hotel rooms and airplane seats are perishable, just like apples and lettuce. When a room or seat is not booked, the company has lost the ability to earn revenue for that night or flight. Setting the right price for the right customer on the right day is complicated. Hotels and airlines feed large data sets into mathematical algorithms that choose the optimal pricing scheme to maximize the revenue for that
room or seat. This practice is called revenue management and is an example of prescriptive analytics. When large data sets are analyzed along with system constraints, companies can quickly simulate many different outcomes related to a wide variety of decisions. This allows the decision makers to choose a set of actions that will result in the best outcome for the company and its customers.
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and Employers (NACE) found that 72 percent of employers ranked “analytical and quantitative skills” as one of the most important attributes for a new hire. When asked to rank the attributes most sought after, employers said that the top seven attributes were (1) communication skills (written), (2) problem-solving skills, (3) ability to work on a team, (4) initiative, (5) analytical/quantitative skills, (6) strong work ethic, and (7) communication skills (verbal). Will
these skills earn you a higher salary? According to the Bureau of Labor Statistics, the median salary for a statistician in 2019 was over $88,000 with job growth projected to be 30 percent over the next 10 years. (See www.bls.gov/ooh/math/mathematicians-andstatisticians.htm.)
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