4th EditionBusiness StatisticsNorean R. SharpeSt. John’s UniversityRichard D. De VeauxWilliams CollegePaul F. VellemanCornell UniversityWith Contributions by David Bockand Special Contributor Eric M. EisensteinA01 SHAR5217 04 SE FM.indd 113/07/18 10:33 AM

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To my loving family for their patience and support—NoreanTo my father, whose daily stories informed me how the worldof business really worked, and to my family, for giving methe love and support that made this book possible—DickTo my father, who taught me about ethical business practice byhis constant example as a small businessman and parent—PaulA01 SHAR5217 04 SE FM.indd 313/07/18 10:33 AM

A01 SHAR5217 04 SE FM.indd 413/07/18 10:33 AM

Meet the AuthorsNorean R. Sharpe, Ph.D., is Dean and the Joseph H. and Maria C. Schwartz DistinguishedChair at The Peter J. Tobin College of Business at St. John’s University. As the chief academicofficer of the Tobin College of Business, she is responsible for the curriculum for 2500 undergraduate business majors and 600 graduate students in one of seven M.S./M.B.A. programs, allsupported by more than 150 faculty and staff on the Manhattan, Queens, Staten Island, andRome, Italy, campuses. Within the Tobin College is the Center for Enterprise Risk Management,the Applied Finance Institute, and the Global Business Stewardship Center, as well as theacclaimed School of Risk Management, Insurance, and Actuarial Science.Dr. Sharpe is an accomplished scholar, with 30 years of teaching experience at Yale University,Bowdoin College, Babson College, and Georgetown University—and with more than 30 scholarly publications in analytics and statistics education. Her research interests include timeseries analysis, forecasting, analytics, and women’s roles in entrepreneurship in the MiddleEast. Dr. Sharpe earned her B.A. from Mt. Holyoke College, her M.S. from the University ofNorth Carolina, and her Ph.D. in Systems Engineering from the University of Virginia.Richard D. De Veaux (Ph.D. Stanford University) is an internationally known educator, con-sultant, and lecturer. Dick has taught statistics at a business school (Wharton), an engineeringschool (Princeton), and a liberal arts college (Williams). While at Princeton, he won a LifetimeAward for Dedication and Excellence in Teaching. Since 1994, he has taught at Williams College,although he returned to Princeton for the academic year 2006–2007 as the William R. KenanJr. Visiting Professor of Distinguished Teaching. He is currently the C. Carlisle and MargaretTippit Professor of Statistics at Williams College. Dick holds degrees from Princeton Universityin Civil Engineering and Mathematics and from Stanford University where he studied statisticswith Persi Diaconis and dance with Inga Weiss. His research focuses on the analysis of largedatasets and data mining in science and industry. Dick has won both the Wilcoxon and Shewellawards from the American Society for Quality. He is an elected member of the InternationalStatistics Institute (ISI) and a Fellow of the American Statistical Association (ASA). Dick waselected Vice President of the ASA in 2018 and will serve from 2019 to 2021. Dick is alsowell known in industry, having consulted for such Fortune 500 companies as American Express,Hewlett-Packard, Alcoa, DuPont, Pillsbury, General Electric, and Chemical Bank. He was namedthe “Statistician of the Year” for 2008 by the Boston Chapter of the American StatisticalAssociation. In his spare time he is an avid cyclist and swimmer, and is a frequent singer andsoloist with various local choirs, including the Choeur Vittoria of Paris, France. Dick is the fatherof four children.Paul F. Velleman (Ph.D. Princeton University) has an international reputation for innovativestatistics education. He designed the Data Desk software package and is also the authorand designer of the award-winning ActivStats multimedia software, for which he received theEDUCOM Medal for innovative uses of computers in teaching statistics and the ICTCM Awardfor Innovation in Using Technology in College Mathematics. He is the founder and CEO of DataDescription, Inc. (, which supports both of these programs. Data Descriptionalso developed and maintains the Internet site Data and Story Library (DASL;, which provides all of the datasets used in this text as well as many others useful forteaching statistics, and the statistics conceptual tools at Paul coauthored(with David Hoaglin) the book ABCs of Exploratory Data Analysis. Paul is Emeritus Professorof Statistical Sciences, at Cornell University where he was awarded the MacIntyre Prize forExemplary Teaching. Paul earned his M.S. and Ph.D. from Princeton University, where he studiedwith John Tukey. His research often focuses on statistical graphics and data analysis methods.Paul is a Fellow of the American Statistical Association and of the American Association for theAdvancement of Science. He was a member of the working group that developed the GAISE2016 guidelines for teaching statistics. Paul’s experience as a professor, entrepreneur, andbusiness leader brings a unique perspective to the book.Richard De Veaux and Paul Velleman have authored successful books in the introductory college and AP High School market with David Bock, including Intro Stats, Fifth Edition (Pearson,2018); Stats: Modeling the World, Fifth Edition (Pearson, 2019); and Stats: Data and Models,Fourth Edition (Pearson, 2016).A01 SHAR5217 04 SE FM.indd 513/07/18 10:33 AM

viMeet the AuthorsSpecial ContributorEric M. Eisenstein (Ph.D. Wharton School of Business) is an internationally knowneducator, researcher, and consultant. Eric has taught at multiple business schools,including Wharton, Cornell’s Johnson School, ESADE, and Temple University’s FoxSchool of Business. At Fox, he serves as the Director of the MS in Business Analyticsin the department of Statistical Science, Director of Graduate Programs in the department of Marketing and Supply Chain Management, and Chair of the UndergraduateProgram (curriculum) Committee. Eric teaches data analytics, quantitative strategy, andmarketing. His research focuses on the psychology of expertise, how to improve decision making, and strategic analytics. Prior to becoming an academic, Eric worked atMercer Management Consulting (now Oliver Wyman) where he focused on managementof technology and marketing research in the financial services and telecommunicationsindustries. His teams won the outstanding team award three times consecutively; clientsinvested over 30 million based on the recommendations of his teams, and the teams’strategic recommendations affected more than 10 billion in revenue and 2 billionin profits. He continues to consult and serve on the board of numerous companiesand charities. Eric earned his Ph.D. in Applied Economics and an M.A. in Statistics atthe Wharton School of Business, University of Pennsylvania and graduated from theManagement and Technology dual degree program at the University of Pennsylvania,where he concurrently earned a B.S. in Economics from Wharton and a B.S. in ComputerSystems Engineering from the School of Engineering and Applied Science. He is theproud father to three children.A01 SHAR5217 04 SE FM.indd 618/07/18 11:24 AM

ContentsPrefaceIndex of ApplicationsPart IChapter 1Chapter 2Chapter 3Chapter 4Part IIChapter 5xiixxviiExploring and Collecting DataData and Decisions (H&M)11.1 Data, 3 1.2 The Role of Data in Decision Making, 5 1.3 Variable Types, 8 1.4 Data Sources: Where, How, and When, 10Ethics in ActionFrom Learning to EarningTech Support: Entering DataBrief Case: Credit Card Bank13141516Visualizing and Describing Categorical Data (Dalia Research)212.1 Summarizing a Categorical Variable, 22 2.2 Displaying a Categorical Variable, 24 2.3 Exploring Relationships Between Two Categorical Variables: ContingencyTables, 28 2.4 Segmented Bar Charts and Mosaic Plots, 30 2.5 Three CategoricalVariables, 37 2.6 Simpson’s Paradox, 39Ethics in ActionFrom Learning to EarningTech Support: Displaying Categorical DataBrief Case: Credit Card Bank41424346Describing, Displaying, and Visualizing Quantitative Data (AIG)563.1 Visualizing Quantitative Variables, 58 3.2 Shape, 60 3.3 Center, 62 3.4 Spread of the Distribution, 64 3.5 Shape, Center, and Spread—ASummary, 67 3.6 Standardizing Variables, 67 3.7 Five-Number Summaryand Boxplots, 69 3.8 Comparing Groups, 72 3.9 Identifying Outliers, 75 3.10 Time Series Plots, 76 *3.11 Transforming Skewed Data, 79Ethics in ActionFrom Learning to EarningTech Support: Displaying and Summarizing Quantitative VariablesBrief Case: Detecting the Housing Bubble84858790Correlation and Linear Regression ( Looking at Scatterplots, 106 4.2 Assigning Roles to Variables in Scatterplots, 109 4.3 Understanding Correlation, 110 4.4 Lurking Variables and Causation, 115 4.5 The Linear Model, 116 4.6 Correlation and the Line, 117 4.7 Regression tothe Mean, 120 4.8 Checking the Model, 121 4.9 Variation in the Model and R 2, 124 4.10 Reality Check: Is the Regression Reasonable? 126 4.11 NonlinearRelationships, 130 *4.12 Multiple Regression—A Glimpse Ahead, 133Ethics in ActionFrom Learning to EarningTech Support: Correlation and RegressionBrief Case: Fuel Efficiency, Cost of Living, and Mutual FundsCase Study: Paralyzed Veterans of America137138139142155Modeling with ProbabilityRandomness and Probability (Credit Reports, the Fair IsaacsCorporation, and Equifax)1575.1 Random Phenomena and Probability, 158 5.2 The Nonexistent Law of Averages, 160 5.3 Different Types of Probability, 161 5.4 Probability Rules, 163 5.5 JointProbability and Contingency Tables, 168 5.6 Conditional Probability and the GeneralMultiplication Rule, 169 5.7 Constructing Contingency Tables, 172 5.8 ProbabilityTrees, 173 *5.9 Reversing the Conditioning: Bayes’ Rule, 175Ethics in ActionFrom Learning to EarningTech Support: Generating Random NumbersBrief Case: Global Markets177177179180viiA01 SHAR5217 04 SE FM.indd 713/07/18 10:33 AM

viiiContentsChapter 6Chapter 7Part IIIChapter 8Chapter 9Random Variables and Probability Models (Metropolitan LifeInsurance Company)1906.1 Expected Value of a Random Variable, 191 6.2 Standard Deviation of a RandomVariable, 194 6.3 Properties of Expected Values and Variances, 197 6.4 BernoulliTrials, 201 6.5 Discrete Probability Models, 201Ethics in ActionFrom Learning to EarningTech Support: Random Variables and Probability ModelsBrief Case: Investment Options209210211212The Normal and Other Continuous Distributions (The NYSE)2207.1 The Standard Deviation as a Ruler, 221 7.2 The Normal Distribution, 223 7.3 Normal Probability Plots, 230 7.4 The Distribution of Sums ofNormals, 231 7.5 The Normal Approximation for the Binomial, 234 7.6 OtherContinuous Random Variables, 237Ethics in ActionFrom Learning to EarningTech Support: Probability Calculations and PlotsBrief Case: Price/Earnings and Stock Value241241242244Gathering DataData Sources: Observational Studies and Surveys(Roper Polls)2528.1 Observational Studies and Found Data, 253 8.2 Sample Surveys, 255 8.3 Populations and Parameters, 259 8.4 Common Sampling Designs, 260 8.5 The Valid Survey, 265 8.6 How to Sample Badly, 267Ethics in ActionFrom Learning to EarningTech SupportBrief Case: Market Survey Research and The GfK Roper Reports Worldwide Survey270270272273Data Sources: Experiments (Capital One)2809.1 Randomized, Comparative Experiments, 283 9.2 The Four Principles ofExperimental Design, 284 9.3 Experimental Designs, 286 9.4 Issues in ExperimentalDesign, 291 9.5 Displaying Data from Designed Experiments, 293Ethics in Action300From Learning to Earning300Brief Case: Design a Multifactor Experiment302Part IVChapter 10Chapter 11A01 SHAR5217 04 SE FM.indd 8Inference for Decision MakingSampling Distributions and Confidence Intervals forProportions (Marketing Credit Cards: The MBNA Story)31010.1 The Distribution of Sample Proportions, 311 10.2 A Confidence Interval for aProportion, 316 10.3 Margin of Error: Certainty vs. Precision, 321 10.4 Choosingthe Sample Size, 325Ethics in ActionFrom Learning to EarningTech Support: Confidence Intervals for ProportionsBrief Case: Has Gold Lost its Luster? and Forecasting DemandCase Study: Real Estate Simulation330330332333343Confidence Intervals for Means (Guinness & Co.)34411.1 The Central Limit Theorem, 345 11.2 The Sampling Distribution of the Mean,349 11.3 How Sampling Distribution Models Work, 350 11.4 Gosset and thet-Distribution, 352 11.5 A Confidence Interval for Means, 354 11.6 Assumptionsand Conditions, 356 11.7 Visualizing Confidence Intervals for the Mean, 363Ethics in ActionFrom Learning to EarningTech Support: Confidence Intervals for MeansBrief Case: Real Estate and Donor Profiles36836837037113/07/18 10:33 AM

Contents ixChapter 12Chapter 13Chapter 14Chapter 15Part VChapter 16Chapter 17A01 SHAR5217 04 SE FM.indd 9Testing Hypotheses (Casting Ingots)38112.1 Hypotheses, 382 12.2 P-Values, 384 12.3 The Reasoning of HypothesisTesting, 387 12.4 A Hypothesis Test for the Mean, 392 12.5 Intervals andTests, 398 12.6 P-Values and Decisions: What to Tell About a Hypothesis Test, 403Ethics in ActionFrom Learning to EarningTech Support: Hypothesis TestsBrief Case: Real Estate and Donor Profiles406406408411More About Tests and Intervals (Traveler’s Insurance)41913.1 How to Think About P-Values, 421 13.2 Alpha Levels and Significance, 426 13.3 Critical Values, 428 13.4 Confidence Intervals and Hypothesis Tests, 429 13.5 Two Types of Errors, 432 13.6 Power, 434Ethics in ActionFrom Learning to EarningBrief Case: Confidence Intervals and Hypothesis Tests438438439Comparing Two Means (Visa Global Organization)44714.1 Comparing Two Means, 448 14.2 The Two-Sample t-Test, 451 14.3 Assumptionsand Conditions, 452 14.4 A Confidence Interval for the Difference Between TwoMeans, 456 14.5 The Pooled t-Test, 458 14.6 Paired Data, 463 14.7 Pairedt-Methods, 464Ethics in ActionFrom Learning to EarningTech Support: Comparing Two GroupsBrief Case: Real Estate and Consumer Spending Patterns (Data Analysis)470470472476Inference for Counts: Chi-Square Tests (SAC Capital)49315.1 Goodness-of-Fit Tests, 495 15.2 Interpreting Chi-Square Values, 499 15.3 Examining the Residuals, 500 15.4 The Chi-Square Test of Homogeneity, 502 15.5 Comparing Two Proportions, 506 15.6 Chi-Square Test of Independence, 507Ethics in ActionFrom Learning to EarningTech Support: Chi-SquareBrief Case: Health Insurance and Loyalty ProgramCase Study: Investment Strategy Segmentation513514515518530Models for Decision MakingInference for Regression (Nambé Mills)53116.1 A Hypothesis Test and Confidence Interval for the Slope, 532 16.2 Assumptionsand Conditions, 536 16.3 Standard Errors for Predicted Values, 542 16.4 UsingConfidence and Prediction Intervals, 545Ethics in ActionFrom Learning to EarningTech Support: Regression AnalysisBrief Case: Frozen Pizza and Global Warming?547547549551Understanding Residuals (Kellogg’s)56517.1 Examining Residuals for Groups, 566 17.2 Extrapolation and Prediction, 569 17.3 Unusual and Extraordinary Observations, 571 17.4 Working with SummaryValues, 575 17.5 Autocorrelation, 576 17.6 Transforming (Re-expressing)Data, 578 17.7 The Ladder of Powers, 582Ethics in ActionFrom Learning to EarningTech Support: Examining ResidualsBrief Case: Gross Domestic Product and Energy Sources58958959059213/07/18 10:33 AM

xContentsChapter 18Chapter 19Multiple Regression ( The Multiple Regression Model, 609 18.2 Interpreting Multiple RegressionCoefficients, 611 18.3 Assumptions and Conditions for the Multiple RegressionModel, 613 18.4 Testing the Multiple Regression Model, 621 18.5 Adjusted R 2 andthe F-statistic, 623 *18.6 The Logistic Regression Model, 625Ethics in ActionFrom Learning to EarningTech Support: Regression AnalysisBrief Case: Golf Success632633634636Building Multiple Regression Models (Bolliger and Mabillard)64819.1 Indicator (or Dummy) Variables, 650 19.2 Adjusting for Different Slopes—InteractionTerms, 654 19.3 Multiple Regression Diagnostics, 657 19.4 Building RegressionModels, 663 19.5 Collinearity, 673 19.6 Quadratic Terms, 676Ethics in Action681From Learning to Earning682Tech Support: Building Multiple Regression Models683Brief Case: Building Models685Chapter 20Part VIChapter 21Time Series Analysis (Whole Foods Market )69720.1 What Is a Time Series? 699 20.2 Components of a Time Series, 699 20.3 Smoothing Methods, 702 20.4 Summarizing Forecast Error, 707 20.5 Autoregressive Models, 709 20.6 Multiple Regression–Based Models, 716 20.7 Choosing a Time Series Forecasting Method, 726 20.8 Interpreting Time SeriesModels: The Whole Foods Data Revisited, 727Ethics in ActionFrom Learning to EarningTech Support: Time SeriesBrief Case: U.S. Trade with the European UnionCase Study: Health Care Costs728728731731745AnalyticsIntroduction to Big Data and Data Mining (ParalyzedVeterans of America)74621.1 Data Mining and the Big Data Revolution, 747 21.2 The Data Mining Process,751 21.3 Data Mining Algorithms: A Sample, 757 21.4 Models Built from CombiningOther Models, 765 21.5 Comparing Models, 768 21.6 Summary, 774Ethics in Action775From Learning to Earning775Part VIIChapter 22Online TopicsQuality Control (Sony)22-122.1 A Short History of Quality Control, 22-3 22.2 Control Charts for IndividualObservations (Run Charts), 22-7 22.3 Control Charts for Measurements: X andR Charts, 22-10 22.4 Actions for Out-of-Control Processes, 22-16 22.5 Control Chartsfor Attributes: p Charts and c Charts, 22-22 22.6 Philosophies of Quality Control, 22-25Ethics in Action22-27From Learning to Earning22-27Tech Support: Quality Control Charts22-29Brief Case: Laptop Touchpad Quality22-30Chapter 23Nonparametric Methods (i4cp)23-123.1 Ranks, 23-2 23.2 The Wilcoxon Rank-Sum/Mann-Whitney Statistic, 23-3 23.3 Kruskal-Wallis Test, 23-7 23.4 Paired Data: The Wilcoxon Signed-RankTest, 23-10 *23.5 Friedman Test for a Randomized Block Design, 23-13 23.6 Kendall’sTau: Measuring Monotonicity, 23-14 23.7 Spearman’s Rho, 23-15 23.8 When ShouldYou Use Nonparametric Methods? 23-16Ethics in Action23-17From Learning to Earning23-18Tech Support: Nonparametric Methods23-19Brief Case: Real Estate Reconsidered23-20A01 SHAR5217 04 SE FM.indd 1025/07/18 9:58 AM

Contents xiChapter 24Decision Making and Risk (Data Description, Inc.)24-124.1 Actions, States of Nature, and Outcomes, 24-2 24.2 Payoff Tables and DecisionTrees, 24-3 24.3 Minimizing Loss and Maximizing Gain, 24-4 24.4 The ExpectedValue of an Action, 24-5 24.5 Expected Value with Perfect Information, 24-7 24.6 Decisions Made with Sample Information, 24-7 24.7 EstimatingVariation, 24-9 24.8 Sensitivity, 24-11 24.9 Simulation, 24-12 24.10 More ComplexDecisions, 24-14Ethics in Action24-14From Learning to Earning24-15Brief Case: Texaco-Pennzoil and Insurance Services, Revisited24-16Chapter 25Analysis of Experiments and Observational Studies25-125.1 Analyzing a Design in One Factor—The One-Way Analysis of Variance, 25-2 25.2 Assumptions and Conditions for ANOVA, 25-6 *25.3 Multiple Comparisons, 25-9 25.4 ANOVA on Observational Data, 25-11 25.5 Analysis of Multifactor Designs, 25-12From Learning to Earning25-21Tech Support: Analysis of Variance25-22Brief Case: Analyze your Multifactor Experiment25-24AppendixesA. AnswersB. Tables and Selected FormulasC. CreditsIndexA01 SHAR5217 04 SE FM.indd 11A-1A-1A-57A-77I-125/07/18 11:40 AM

PrefaceThe question that should motivate a business student’s study of statistics should be“Even without perfect information, how can I make better decisions?”1 As entrepreneurs and consultants, we know that in today’s data-rich environment, knowledge of statistics is essential to survive and thrive in the business world. But, aseducators, we’ve seen a disconnect between the way business statistics is traditionally taught and the way it should be used in making business decisions. In Business Statistics, we try to narrow the gap between theory and practice by presentingrelevant statistical methods that will empower business students to make effective,data-informed decisions.Of course, students should come away from their statistics course knowinghow to think statistically and how to apply statistics methods with modern technology. But they must also be able to communicate their analyses effectively to others.When asked about statistics education, a group of CEOs from Fortune 500 companies recently said that although they were satisfied with the technical competenceof students who had studied statistics, they found the students’ ability to communicate their findings to be woefully inadequate.Our Plan, Do, Report rubric provides a structure for solving business problemsthat mimics the correct application of statistics to solving real business problems.Unlike many other authors, we emphasize the often neglected thinking (Plan) andcommunication (Report) steps in problem solving in addition to the methodology (Do). This approach requires up-to-date, real-world examples and data. So weconstantly strive to illustrate our lessons with current business issues and examples.What’s New in This Edition?We’ve been delighted with the reaction to previous editions of Business Statistics.We’ve made some changes to the organization of the fourth edition to help studentsfocus on the essentials and think about the data-rich world they will find in theworkplace. And, of course, we continue to update examples and exercises so that thestory we tell is always tied to the ways statistics informs modern business practice. Recent data. We teach with real data whenever possible, so we’ve updateddata throughout the book. New examples ref lect current stories in the newsand recent economic and business events. When a historical dataset is especially good at illuminating a pedagogical point, we have, from time to time,chosen pedagogy over recency. Improved organization. We have retained our “data first” presentation oftopics because we find that it provides students with both motivation and afoundation in real business decisions on which to build an understanding. Chapters 1–4 have been streamlined to cover collecting, displaying,summarizing, and understanding data in four chapters. We find that thisprovides students with a solid foundation to launch their study of probability and statistics. Chapters 5–7 introduce students to randomness and probability models.We’ve moved the discussion of probability trees and Bayes’ rule intothese chapters. Chapters 8 and 9 cover data collection by survey and by designed experiments. New discussions here address technology-enabled sampling,online data, and Big Data. We’ve moved the discussion of experimentsup front because of the increased importance of online testing, but we’ve1Unfortunately, not the question most students are asking themselves on the first day of the course.xiiA01 SHAR5217 04 SE FM.indd 1213/07/18 10:33 AM

Preface xiiimoved the analysis of such designs (ANOVA), which many instructorsfind difficult to cover in a first course, to the online Chapter 25. Chapters 10–15 cover inference for both proportions and means. Weintroduce inference by discussing proportions because most students arebetter acquainted with proportions reported in surveys and news stories.However, this edition ties in the discussion of means immediately sostudents can appreciate that the reasoning of inference is the same ina variety of contexts. We’ve added an optional discussion of bootstrapping. This may help students’ intuition about inference as well as providing a relatively new modern method. Chapters 16–19 cover regression-based models for decision making. Chapter 20 discusses time series methods. Chapter 21 is a newly expanded discussion of data mining and Big Data. Chapters 22–24 discuss special topics that can be selected according tothe needs of the course and the preferences of the instructor. Streamlined design. Our goal has always been a readable text. This editionsports a new design that clarifies the purpose of each text element. The majortheme of each chapter is linear and easy to follow without distraction. Supporting material is clearly boxed and shaded, so students know where to focustheir study efforts. Enhanced Technology Help. We’ve updated Technology Help (now calledTech Support) in almost every chapter. Updated examples to reflect the changing world. The time since our lastrevision has seen marked changes in the U.S. and world economies. This hasrequired us to update many of our examples. Our selection of course contentref lects the wisdom of the GAISE2016 report adopted by the American Statistical Association as a standard for introductory statistics teaching. Our “InPractice” elements have all been re-structured to ref lect real-world businesschallenges. The result is a text that is realistic and useful. Increased focus on core material. Statistics in practice means making smartdecisions based on data. Students need to know the methods, how to applythem, and the assumption

vii Contents Preface xii Index of Applications xxvii Part I Exploring and Collecting Data Chapter 1 Data and Decisions (H&M) 1 1.1 Data, 3 1.2 The Role of Data in Decision Making, 5 1.3 Variable Types, 8 1.4 Data Sources: Where, How, and When, 10 Ethics in Action 13 From Learning to Earning 14 Tech