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# A first course in business statistics

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### A first course in business statistics

1. 1. Normal Curve AreasILSource: Abridged from Table I of A. Hald, Statistrcal Tables and Formulas (New York: Wiley), 1952. Reproduced bypermission of A. Hald.
2. 2. Critical Values of t - 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645Source: . IUC with the ~dpermission of the Itustees of Biometril from E. S. Pearson and ,edH. 0. Tablesfor Stat~st~crans, 1,3d ed ,Biometrika, 1966. Hartley (eds), The B~ometnka Vol.
3. 3. A FIRST C O U R S E IN BUSINESS ...................................................................................................................................................................,.............,.......................- Eighth Edition J A M E S T. M c C L A V E Info Tech, Inc. University of FloridaiI P. GEORGE B E N S O N Terry College of BusinessI University of GeorgiaII TERRY S l N C l C H University of South FloridaII PRENTICE HALL Upper Saddle River, NJ 07458
4. 4. "W PROBABILITY 11 7 3.1 Events, Sample Spaces, and Probability 118 3.2 Unions and Intersections 130 3.3 Complementary Events 134 3.4 The Additive Rule and Mutually Exclusive Events 135 3.5 Conditional Probability 140 3.6 The Multiplicative Rule and Independent Events 144 3.7 Random Sampling 154 Statistics in Action: Lottery Buster 158 Quick Review 158 *"ss""ms,"ms%"- W".""""" * " .bb " "* "" . " m . * P RIABLES AND PROBABILITY DISTRIBUTIONS 167 4.1 Two Types of Random Variables 168I 4.2 Probability Distributions for Discrete Random Variables 171 4.3 The Binomial Distribution 181 4.4 The Poisson Distribution (Optional) 194 4.5 Probability Distributions for Continuous RandomI Variables 201 4.6 The Uniform Distribution (Optional) 202 4.7 The Normal Distribution 206 4.8 Descriptive Methods for Assessing Normality 219 4.9 Approximating a Binomial Distribution with a Normal Distribution (Optional) 225 4.10 The Exponential Distribution (Optional) 231 4.11 Sampling Distributions 236 4.12 The Central Limit Theorem 242 Statistics in Action: IQ, Economic Mobility, and the Bell Curve 251 Quick Review 252 Real-World Case: The Furniture Fire Case (A Case Covering Chapters 3-4) 257
5. 5. CONTENTS vii sms-*w " "bums INFERENCES BASED ON A SINGLE SAMPLE: ESTIMATION WITH CONFIDENCE INTERVALS 259 5.1 Large-Sample Confidence Interval for a Population Mean 260 5.2 Small-Sample Confidence Interval for a Population Mean 268I 5.3 Large-Sample Confidence Interval for a PopulationI Proportion 279I 5.4 Determining the Sample Size 286I Statistics in Action: Scallops, Sampling, and the Law 292 Quick Review 293I ma"-mum""-"% " m-"us m"-w--t-""m m ""a","- ""rn *""m%*"-"I ASED ON A SINGLEI+I TESTS OF HYPOTHESIS 299 6.1 The Elements of a Test of Hypothesis 300if a 6.2 Large-Sample Test of Hypothesis About a Population Mean 306 6.3 Observed Significance Levels:p-Values 313 6.4 Small-Sample Test of Hypothesis About a Population Mean 319 6.5 Large-Sample Test of Hypothesis About a PopulationI Proportion 326I 6.6 A Nonparametric Test About a Population Median (Optional) 332i Statistics in Action: March Madness-Handicapping Quick Review 338 the NCAA Basketball Tourney 338 "s,,,m*x- -"a"I COMPARING POPULATION MEANS 345 7.1 Comparing Two Population Means: Independent Sampling 346 7.2 Comparing Two Population Means: Paired Difference Experiments 362I 7.3 Determining the Sample Size 374
6. 6. viii CONTENTS 7.4 Testing the Assumption of Equal Population Variances (Optional) 377 7.5 A Nonparametric Test for Comparing Two Populations: Independent Sampling (Optional) 384 7.6 A Nonparametric Test for Comparing Two Populations: Paired Difference Experiment (Optional) 393 7.7 Comparing Three or More Population Means: Analysis of Variance (Optional) 400 Statistics in Action: On the Trail of the Cockroach 41 6 Quick Review 418 Real-World Case: The Kentucky Milk Case-Part I I (A Case Covering Chapters 5-7) 426 8.1 Comparing Two Population Proportions: Independent Sampling 428 8.2 Determining the Sample Size 435 8.3 Comparing Population Proportions: Multinomial Experiment 437 8.4 Contingency Table Analysis 445 Statistics in Action: Ethics in Computer Technology and Use 458 Quick Review 461 Real-World Case: Discrimination in the Workplace (A Case Covering Chapter 8) 468 9.1 Probabilistic Models 472 9.2 Fitting the Model: The Least Squares Approach 476- 9.3 Model Assumptions 489 9.4 An Estimator of a2 490- 9.5 Assessing the Utility of the Model: Making Inferences About the Slope PI 494 9.6 The Coefficient of Correlation 505- 9.7 The Coefficient of Determination 509
7. 7. 9.8 Using the Model for Estimation and Prediction 516 9.9 Simple Linear Regression: A Complete Example 529 9.10 A Nonparametric Test for Correlation (Optional) 532Statistics in Action: Can "Dowsers" Really Detect Water? 540 Quick Review 544 INTRODUCTION TO MULTIPLE REGRESSION 557 10.1 Multiple Regression Models 558 i / 10.2 The First-Order Model: Estimating and Interpreting the p Parameters 559 10.3 Model Assumptions 565 10.4 Inferences About the P Parameters 568 10.5 Checking the Overall Utility of a Model 580 10.6 Using the Model for Estimation and Prediction 593 10.7 Residual Analysis: Checking the Regression Assumptions 598 10.8 Some Pitfalls: Estimability, Multicollinearity, and Extrapolation 614Statistics in Action: "Wringing" The Bell Curve 624 Quick Review 626 Real-World Case: The Condo Sales Case (A Case Covering Chapters 9-1 0) 634 11.1 Quality, Processes, and Systems 638 11.2 Statistical Control 642 11.3 The Logic of Control Charts 651 11.4 A Control Chart for Monitoring the Mean of a Process: The T-Chart 655 11.5 A Control Chart for Monitoring the Variation of a Process: The R-Chart 672 11.6 A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart 683
8. 8. Statistics in Action: Demings 14 Points 692 Quick Review 694 Real-World Case: The Casket Manufacturing Case (A Case Covering Chapter 11) 699 APPENDIXB Tables 707 AP PEN D l X C Calculation Formulas for Analysis of Variance: Independent Sampling 739 ANSWERS TO SELECTED EXERCISES 741 References 747 Index 753
9. 9. ",: r This eighth edition of A First Course in Business Statistics is an introductory business text emphasizing inference, with extensive coverage of data collection and analysis as needed to evaluate the reported results of statistical studies and to make good decisions. As in earlier editions, the text stresses the development of statistical thinking, the assessment of credibility and value of the inferences made from data, both by those who consume and those who produce them. It assumes a mathematical background of basic algebra. A more comprehensive version of the book, Statistics for Business and Eco- nomics (8/e), is available for two-term courses or those that include more exten- sive coverage of special topics. NEW IN THE EIGHTH EDITION Major Content Changes Chapter 2 includes two new optional sections: methods for detecting outliers (Section 2.8) and graphing bivariate relationships (Section 2.9). Chapter 4 now covers descriptive methods for assessing whether a data set is ap- proximately normally distributed (Section 4.8) and normal approximation to the binomial distribution (Section 4.9). Exploring Data with Statistical Computer Software and the Graphing Calculator- Throughout the text, computer printouts from five popular Windows-based statistical software packages (SAS, SPSS, MINITAB, STATISTIX and EXCEL) are displayed and used to make decisions about the data. New to this edition, we have included instruction boxes and output for the TI-83 graph- ing calculator. Statistics in Action-One feature per chapter examines current real-life, high- profile issues. Data from the study is presented for analysis. Questions prompt the students to form their own conclusions and to think through the statistical issues involved. Real-World Business Cases-Six extensive business problem-solving cases, with real data and assignments. Each case serves as a good capstone and review of the material that has preceded it. Real-Data Exercises-Almost all the exercises in the text employ the use of cur- rent real data taken from a wide variety of publications (e.g., newspapers, magazines, and journals). Quick Review-Each chapter ends with a list of key terms and formulas, with ref- erence to the page number where they first appear. Language Lab-Following the Quick Review is a pronunciation guide for Greek letters and other special terms. Usage notes are also provided.
10. 10. xii TRADITIONAL STRENGTHS We have maintained the features of A First Course in Business Statistics that we believe make it unique among business statistics texts. These features, which assist the student in achieving an overview of statistics and an understanding of its rel- evance in the business world and in everyday life, are as follows: The Use of Examples as a Teaching Device Almost all new ideas are introduced and illustrated by real data-based applica- tions and examples. We believe that students better understand definitions, gen- eralizations, and abstractions after seeing an application. Many Exercises-Labeled by Type The text includes more than 1,000 exercises illustrated by applications in almost all areas of research. Because many students have trouble learning the mechanics of statistical techniques when problems are couched in terms of realistic applica- tions, all exercise sections are divided into two parts: Learning the Mechanics. Designed as straightforward applications of new concepts, these exercises allow students to test their ability to comprehend a concept or a definition. Applying the Concepts. Based on applications taken from a wide variety of jour- nals, newspapers, and other sources, these exercises develop the students skills to comprehend real-world problems and describe situations to which the tech- niques may be applied. A Choice in Level of Coverage of Probability (Chapter 3) One of the most troublesome aspects of an introductory statistics course is the study of probability. Probability poses a challenge for instructors because they must decide on the level of presentation, and students find it a difficult subject to comprehend.We believe that one cause for these problems is the mixture of probability and counting rules that occurs in most introductory texts. We have included the counting rules and worked examples in a separate appendix (Appendix A) at the end of the text. Thus, the instructor can control the level of coverage of probability. Nonparametric Topics Integrated In a one-term course it is often difficult to find time to cover nonparametric tech- niques when they are relegated to a separate chapter at the end of the book. Conse- quently,we have integrated the most commonly used techniques in optional sections as appropriate. Coverage of Multiple Regression Analysis (Chapter 10) This topic represents one of the most useful statistical tools for the solution of ap- plied problems. Although an entire text could be devoted to regression modeling, we believe we have presented coverage that is understandable, usable, and much more comprehensive than the presentations in other introductory statistics texts.
11. 11. ,. Footnotes Although the text is designed for students with a non-calculus background, foot- notes explain the role of calculus in various derivations. Footnotes are also used to inform the student about some of the theory underlying certain results. The foot- notes allow additional flexibility in the mathematical and theoretical level at which the material is presented. S U P P L E M E N T S FOR THE INSTRUCTOR The supplements for the eighth edition have been completely revised to reflect the revisions of the text. To ensure adherence to the approaches presented in the main text, each element in the package has been accuracy checked for clarity and freedom from computational, typographical, and statistical errors. Annotated Instructors Edition (AIE) (ISBN 0-13-027985-4) Marginal notes placed next to discussions of essential teaching concepts include:1I Teaching Tips-suggest alternative presentations or point out common stu- dent errors Exercises-reference specific section and chapter exercises that reinforce the concept H-disk icon identifies data sets and file names of material found on the data CD-ROM in the back of the book. Short Answers-section and chapter exercise answers are provided next to the selected exercises Instructors Notes by Mark Dummeldinger (ISBN 0-13-027410-0) This printed resource contains suggestions for using the questions at the end of the Statistics in Action boxes as the basis for class discussion on statistical ethics and other current issues, solutions to the Real-World Cases, a complete short answer book with letter of permission to duplicate for student usc, and many of the exercises and solutions that were removed from previous editions of this text. Instructors Solutions Manual by Nancy S. Boudreau (ISBN 0-1 3-027421 -6) Solutions to all of the even-numbered exercises are given in this manual. Careful attention has been paid to ensure that all methods of solution and notation are consistent with those used in the core text. Solutions to the odd-numbered exer- cises are found in the Students Solutions Manual. Test Bank by Mark Dummeldinger (ISBN 0-1 3-027419-4) Entirely rewritten, the Test Bank now includes more than 1,000 problems that cor- relate to problems presented in the text.