Statistics for Business and Economics

Openmirrors. com CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Cumulative probability Entries in this table give the area under the curve to the left of the z value. For example, for z = –. 85, the cumulative probability is . 1977. z 0 z 3. 0 2. 9 2. 8 2. 7 2. 6 2. 5 2. 4 2. 3 2. 2 2. 1 2. 0 1. 9 1. 8 1. 7 1. 6 1. 5 1. 4 1. 3 1. 2 1. 1 1. 0 . 9 . 8 . 7 . 6 . 5 . 4 . 3 . 2 . 1 . 0 .00 . 0013 . 0019 . 0026 . 0035 . 0047 . 0062 . 0082 . 0107 . 0139 . 0179 . 0228 . 0287 . 0359 . 0446 . 0548 . 0668 . 0808 . 0968 . 1151 . 1357 . 1587 . 1841 . 2119 . 2420 . 2743 . 3085 . 3446 . 3821 . 4207 . 4602 . 5000 01 . 0013 . 0018 . 0025 . 0034 . 0045 . 0060 . 0080 . 0104 . 0136 . 0174 . 0222 . 0281 . 0351 . 0436 . 0537 . 0655 . 0793 . 0951 . 1131 . 1335 . 1562 . 1814 . 2090 . 2389 . 2709 . 3050 . 3409 . 3783 . 4168 . 4562 . 4960 .02 . 0013 . 0018 . 0024 . 0033 . 0044 . 0059 . 0078 . 0102 . 0132 . 0170 . 0217 . 0274 . 0344 . 0427 . 0526 . 0643 . 0778 . 0934 . 1112 . 1314 . 1539 . 1788 . 2061 . 2358 . 2676 . 3015 . 3372 . 3745 . 4129 . 4522 . 4920 .03 . 0012 . 0017 . 0023 . 0032 . 0043 . 0057 . 0075 . 0099 . 0129 . 0166 . 0212 . 0268 . 0336 . 0418 . 0516 . 0630 . 0764 . 0918 . 1093 . 1292 . 1515 . 1762 . 2033 . 2327 . 643 . 2981 . 3336 . 3707 . 4090 . 4483 . 4880 .04 . 0012 . 0016 . 0023 . 0031 . 0041 . 0055 . 0073 . 0096 . 0125 . 0162 . 0207 . 0262 . 0329 . 0409 . 0505 . 0618 . 0749 . 0901 . 1075 . 1271 . 1492 . 1736 . 2005 . 2296 . 2611 . 2946 . 3300 . 3669 . 4052 . 4443 . 4840 .05 . 0011 . 0016 . 0022 . 0030 . 0040 . 0054 . 0071 . 0094 . 0122 . 0158 . 0202 . 0256 . 0322 . 0401 . 0495 . 0606 . 0735 . 0885 . 1056 . 1251 . 1469 . 1711 . 1977 . 2266 . 2578 . 2912 . 3264 . 3632 . 4013 . 4404 . 4801 .06 . 0011 . 0015 . 0021 . 0029 . 0039 . 0052 . 0069 . 0091 . 0119 . 0154 . 0197 . 0250 . 0314 . 0392 . 0485 . 0594 . 0721 . 0869 . 038 . 1230 . 1446 . 1685 . 1949 . 2236 . 2546 . 2877 . 3228 . 3594 . 3974 . 4364 . 4761 .07 . 0011 . 0015 . 0021 . 0028 . 0038 . 0051 . 0068 . 0089 . 0116 . 0150 . 0192 . 0244 . 0307 . 0384 . 0475 . 0582 . 0708 . 0853 . 1020 . 1210 . 1423 . 1660 . 1922 . 2206 . 2514 . 2843 . 3192 . 3557 . 3936 . 4325 . 4721 .08 . 0010 . 0014 . 0020 . 0027 . 0037 . 0049 . 0066 . 0087 . 0113 . 0146 . 0188 . 0239 . 0301 . 0375 . 0465 . 0571 . 0694 . 0838 . 1003 . 1190 . 1401 . 1635 . 1894 . 2177 . 2483 . 2810 . 3156 . 3520 . 3897 . 4286 . 4681 .09 . 0010 . 0014 . 0019 . 0026 . 0036 . 0048 . 0064 . 0084 . 0110 . 0143 . 0183 . 0233 . 294 . 0367 . 0455 . 0559 . 0681 . 0823 . 0985 . 1170 . 1379 . 1611 . 1867 . 2148 . 2451 . 2776 . 3121 . 3483 . 3859 . 4247 . 4641 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Cumulative probability Entries in the table give the area under the curve to the left of the z value. For example, for z = 1. 25, the cumulative probability is . 8944. 0 z z . 0 . 1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 1. 0 1. 1 1. 2 1. 3 1. 4 1. 5 1. 6 1. 7 1. 8 1. 9 2. 0 2. 1 2. 2 2. 3 2. 4 2. 5 2. 6 2. 7 2. 8 2. 9 3. 0 .00 . 5000 . 5398 . 5793 . 6179 . 6554 . 6915 . 7257 . 7580 . 7881 . 8159 . 8413 . 8643 . 8849 . 9032 . 192 . 9332 . 9452 . 9554 . 9641 . 9713 . 9772 . 9821 . 9861 . 9893 . 9918 . 9938 . 9953 . 9965 . 9974 . 9981 . 9987 .01 . 5040 . 5438 . 5832 . 6217 . 6591 . 6950 . 7291 . 7611 . 7910 . 8186 . 8438 . 8665 . 8869 . 9049 . 9207 . 9345 . 9463 . 9564 . 9649 . 9719 . 9778 . 9826 . 9864 . 9896 . 9920 . 9940 . 9955 . 9966 . 9975 . 9982 . 9987 .02 . 5080 . 5478 . 5871 . 6255 . 6628 . 6985 . 7324 . 7642 . 7939 . 8212 . 8461 . 8686 . 8888 . 9066 . 9222 . 9357 . 9474 . 9573 . 9656 . 9726 . 9783 . 9830 . 9868 . 9898 . 9922 . 9941 . 9956 . 9967 . 9976 . 9982 . 9987 .03 . 5120 . 5517 . 5910 . 6293 . 6664 . 7019 . 7357 . 7673 . 967 . 8238 . 8485 . 8708 . 8907 . 9082 . 9236 . 9370 . 9484 . 9582 . 9664 . 9732 . 9788 . 9834 . 9871 . 9901 . 9925 . 9943 . 9957 . 9968 . 9977 . 9983 . 9988 .04 . 5160 . 5557 . 5948 . 6331 . 6700 . 7054 . 7389 . 7704 . 7995 . 8264 . 8508 . 8729 . 8925 . 9099 . 9251 . 9382 . 9495 . 9591 . 9671 . 9738 . 9793 . 9838 . 9875 . 9904 . 9927 . 9945 . 9959 . 9969 . 9977 . 9984 . 9988 .05 . 5199 . 5596 . 5987 . 6368 . 6736 . 7088 . 7422 . 7734 . 8023 . 8289 . 8531 . 8749 . 8944 . 9115 . 9265 . 9394 . 9505 . 9599 . 9678 . 9744 . 9798 . 9842 . 9878 . 9906 . 9929 . 9946 . 9960 . 9970 . 9978 . 9984 . 9989 .06 . 5239 . 636 . 6026 . 6406 . 6772 . 7123 . 7454 . 7764 . 8051 . 8315 . 8554 . 8770 . 8962 . 9131 . 9279 . 9406 . 9515 . 9608 . 9686 . 9750 . 9803 . 9846 . 9881 . 9909 . 9931 . 9948 . 9961 . 9971 . 9979 . 9985 . 9989 .07 . 5279 . 5675 . 6064 . 6443 . 6808 . 7157 . 7486 . 7794 . 8078 . 8340 . 8577 . 8790 . 8980 . 9147 . 9292 . 9418 . 9525 . 9616 . 9693 . 9756 . 9808 . 9850 . 9884 . 9911 . 9932 . 9949 . 9962 . 9972 . 9979 . 9985 . 9989 .08 . 5319 . 5714 . 6103 . 6480 . 6844 . 7190 . 7517 . 7823 . 8106 . 8365 . 8599 . 8810 . 8997 . 9162 . 9306 . 9429 . 9535 . 9625 . 9699 . 9761 . 9812 . 9854 . 9887 . 9913 . 9934 . 9951 . 963 . 9973 . 9980 . 9986 . 9990 .09 . 5359 . 5753 . 6141 . 6517 . 6879 . 7224 . 7549 . 7852 . 8133 . 8389 . 8621 . 8830 . 9015 . 9177 . 9319 . 9441 . 9545 . 9633 . 9706 . 9767 . 9817 . 9857 . 9890 . 9916 . 9936 . 9952 . 9964 . 9974 . 9981 . 9986 . 9990 STATISTICS FOR BUSINESS AND ECONOMICS 11e This page intentionally left blank STATISTICS FOR BUSINESS AND ECONOMICS 11e David R. Anderson University of Cincinnati Dennis J. Sweeney University of Cincinnati Thomas A. Williams Rochester Institute of Technology Statistics for Business and Economics, Eleventh Edition David R. Anderson, Dennis J. Sweeney, Thomas A.
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Macintosh and Power Macintosh are registered trademarks of Apple Computer, Inc. used herein under license. Library of Congress Control Number: 2009932190 Student Edition ISBN 13: 978-0-324-78325-4 Student Edition ISBN 10: 0-324-78325-6 Instructor’s Edition ISBN 13: 978-0-538-45149-9 Instructor’s Edition ISBN 10: 0-538-45149-1 South-Western Cengage Learning 5191 Natorp Boulevard Mason, OH 45040 USA Cengage Learning products are represented in Canada by Nelson Education, Ltd.
For your course and learning solutions, visit www. cengage. com Purchase any of our products at your local college store or at our preferred online store www. ichapters. com Printed in the United States of America 1 2 3 4 5 6 7 13 12 11 10 09 Dedicated to Marcia, Cherri, and Robbie This page intentionally left blank Brief Contents
Preface xxv About the Authors xxix Chapter 1 Data and Statistics 1 Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations 31 Chapter 3 Descriptive Statistics: Numerical Measures 85 Chapter 4 Introduction to Probability 148 Chapter 5 Discrete Probability Distributions 193 Chapter 6 Continuous Probability Distributions 232 Chapter 7 Sampling and Sampling Distributions 265 Chapter 8 Interval Estimation 308 Chapter 9 Hypothesis Tests 348 Chapter 10 Inference About Means and Proportions with Two Populations 406 Chapter 11 Inferences About Population Variances 448 Chapter 12 Tests of Goodness of Fit and Independence 472 Chapter 13 Experimental Design and Analysis of Variance 506 Chapter 14 Simple Linear Regression 560 Chapter 15 Multiple Regression 642 Chapter 16 Regression Analysis: Model
Building 712 Chapter 17 Index Numbers 763 Chapter 18 Time Series Analysis and Forecasting 784 Chapter 19 Nonparametric Methods 855 Chapter 20 Statistical Methods for Quality Control 903 Chapter 21 Decision Analysis 937 Chapter 22 Sample Survey On Website Appendix A References and Bibliography 976 Appendix B Tables 978 Appendix C Summation Notation 1005 Appendix D Self-Test Solutions and Answers to Even-Numbered Exercises 1007 Appendix E Using Excel Functions 1062 Appendix F Computing p-Values Using Minitab and Excel 1067 Index 1071 This page intentionally left blank Contents Preface xxv About the Authors xxix Chapter 1 Data and Statistics 1 Statistics in Practice: BusinessWeek 2 1. 1 Applications in Business and Economics 3 Accounting 3 Finance 4 Marketing 4 Production 4 Economics 4 1. Data 5 Elements, Variables, and Observations 5 Scales of Measurement 6 Categorical and Quantitative Data 7 Cross-Sectional and Time Series Data 7 1. 3 Data Sources 10 Existing Sources 10 Statistical Studies 11 Data Acquisition Errors 13 1. 4 Descriptive Statistics 13 1. 5 Statistical Inference 15 1. 6 Computers and Statistical Analysis 17 1. 7 Data Mining 17 1. 8 Ethical Guidelines for Statistical Practice 18 Summary 20 Glossary 20 Supplementary Exercises 21 Appendix: An Introduction to StatTools 28 Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations 31 Statistics in Practice: Colgate-Palmolive Company 32 2. 1 Summarizing Categorical Data 33 Frequency Distribution 33 Relative Frequency and Percent Frequency Distributions 34 Bar Charts and Pie Charts 34 x Contents 2. Summarizing Quantitative Data 39 Frequency Distribution 39 Relative Frequency and Percent Frequency Distributions 41 Dot Plot 41 Histogram 41 Cumulative Distributions 43 Ogive 44 2. 3 Exploratory Data Analysis: The Stem-and-Leaf Display 48 2. 4 Crosstabulations and Scatter Diagrams 53 Crosstabulation 53 Simpson’s Paradox 56 Scatter Diagram and Trendline 57 Summary 63 Glossary 64 Key Formulas 65 Supplementary Exercises 65 Case Problem 1: Pelican Stores 71 Case Problem 2: Motion Picture Industry 72 Appendix 2. 1 Using Minitab for Tabular and Graphical Presentations 73 Appendix 2. 2 Using Excel for Tabular and Graphical Presentations 75 Appendix 2. 3 Using StatTools for Tabular and Graphical Presentations 84 Chapter 3 Descriptive Statistics: Numerical Measures 85 Statistics in Practice: Small Fry Design 86 3. Measures of Location 87 Mean 87 Median 88 Mode 89 Percentiles 90 Quartiles 91 3. 2 Measures of Variability 95 Range 96 Interquartile Range 96 Variance 97 Standard Deviation 99 Coefficient of Variation 99 3. 3 Measures of Distribution Shape, Relative Location, and Detecting Outliers 102 Distribution Shape 102 z-Scores 103 Chebyshev’s Theorem 104 Empirical Rule 105 Detecting Outliers 106 Contents xi 3. 4 Exploratory Data Analysis 109 Five-Number Summary 109 Box Plot 110 3. 5 Measures of Association Between Two Variables 115 Covariance 115 Interpretation of the Covariance 117 Correlation Coefficient 119 Interpretation of the Correlation Coefficient 120 3. The Weighted Mean and Working with Grouped Data 124 Weighted Mean 124 Grouped Data 125 Summary 129 Glossary 130 Key Formulas 131 Supplementary Exercises 133 Case Problem 1: Pelican Stores 137 Case Problem 2: Motion Picture Industry 138 Case Problem 3: Business Schools of Asia-Pacific 139 Case Problem 4: Heavenly Chocolates Website Transactions 139 Appendix 3. 1 Descriptive Statistics Using Minitab 142 Appendix 3. 2 Descriptive Statistics Using Excel 143 Appendix 3. 3 Descriptive Statistics Using StatTools 146 Chapter 4 Introduction to Probability 148 Statistics in Practice: Oceanwide Seafood 149 4. 1 Experiments, Counting Rules, and Assigning Probabilities 150 Counting Rules, Combinations, and Permutations 151 Assigning Probabilities 155 Probabilities for the KP&L Project 157 4. 2 Events and Their Probabilities 160 4. 3 Some Basic Relationships of Probability 164 Complement of an Event 164 Addition Law 165 4. 4 Conditional Probability 171 Independent Events 174 Multiplication Law 174 4. Bayes’ Theorem 178 Tabular Approach 182 Summary 184 Glossary 184 xii Contents Key Formulas 185 Supplementary Exercises 186 Case Problem: Hamilton County Judges 190 Chapter 5 Discrete Probability Distributions 193 Statistics in Practice: Citibank 194 5. 1 Random Variables 194 Discrete Random Variables 195 Continuous Random Variables 196 5. 2 Discrete Probability Distributions 197 5. 3 Expected Value and Variance 202 Expected Value 202 Variance 203 5. 4 Binomial Probability Distribution 207 A Binomial Experiment 208 Martin Clothing Store Problem 209 Using Tables of Binomial Probabilities 213 Expected Value and Variance for the Binomial Distribution 214 5. Poisson Probability Distribution 218 An Example Involving Time Intervals 218 An Example Involving Length or Distance Intervals 220 5. 6 Hypergeometric Probability Distribution 221 Summary 225 Glossary 225 Key Formulas 226 Supplementary Exercises 227 Appendix 5. 1 Discrete Probability Distributions with Minitab 230 Appendix 5. 2 Discrete Probability Distributions with Excel 230 Chapter 6 Continuous Probability Distributions 232 Statistics in Practice: Procter & Gamble 233 6. 1 Uniform Probability Distribution 234 Area as a Measure of Probability 235 6. 2 Normal Probability Distribution 238 Normal Curve 238 Standard Normal Probability Distribution 40 Computing Probabilities for Any Normal Probability Distribution 245 Grear Tire Company Problem 246 6. 3 Normal Approximation of Binomial Probabilities 250 6. 4 Exponential Probability Distribution 253 Computing Probabilities for the Exponential Distribution 254 Relationship Between the Poisson and Exponential Distributions 255 Contents xiii Summary 257 Glossary 258 Key Formulas 258 Supplementary Exercises 258 Case Problem: Specialty Toys 261 Appendix 6. 1 Continuous Probability Distributions with Minitab 262 Appendix 6. 2 Continuous Probability Distributions with Excel 263 Chapter 7 Sampling and Sampling Distributions 265 Statistics in Practice: MeadWestvaco Corporation 266 7. 1 The Electronics Associates Sampling Problem 267 7. Selecting a Sample 268 Sampling from a Finite Population 268 Sampling from an Infinite Population 270 7. 3 Point Estimation 273 Practical Advice 275 7. 4 Introduction to Sampling Distributions 276 _ 7. 5 Sampling Distribution of x 278 _ Expected Value of x 279 _ Standard Deviation of x 280 _ Form of the Sampling Distribution of x 281 _ Sampling Distribution of x for the EAI Problem 283 _ Practical Value of the Sampling Distribution of x 283 Relationship Between the Sample Size and the Sampling _ Distribution of x 285 _ 7. 6 Sampling Distribution of p 289 _ Expected Value of p 289 _ Standard Deviation of p 290 _ Form of the Sampling Distribution of p 291 _ Practical Value of the Sampling Distribution of p 291 7. Properties of Point Estimators 295 Unbiased 295 Efficiency 296 Consistency 297 7. 8 Other Sampling Methods 297 Stratified Random Sampling 297 Cluster Sampling 298 Systematic Sampling 298 Convenience Sampling 299 Judgment Sampling 299 Summary 300 Glossary 300 Key Formulas 301 xiv Contents Supplementary Exercises 302 _ Appendix 7. 1 The Expected Value and Standard Deviation of x 304 Appendix 7. 2 Random Sampling with Minitab 306 Appendix 7. 3 Random Sampling with Excel 306 Appendix 7. 4 Random Sampling with StatTools 307 Chapter 8 Interval Estimation 308 Statistics in Practice: Food Lion 309 8. 1 Population Mean: Known 310 Margin of Error and the Interval Estimate 310 Practical Advice 314 8. Population Mean: Unknown 316 Margin of Error and the Interval Estimate 317 Practical Advice 320 Using a Small Sample 320 Summary of Interval Estimation Procedures 322 8. 3 Determining the Sample Size 325 8. 4 Population Proportion 328 Determining the Sample Size 330 Summary 333 Glossary 334 Key Formulas 335 Supplementary Exercises 335 Case Problem 1: Young Professional Magazine 338 Case Problem 2: Gulf Real Estate Properties 339 Case Problem 3: Metropolitan Research, Inc. 341 Appendix 8. 1 Interval Estimation with Minitab 341 Appendix 8. 2 Interval Estimation with Excel 343 Appendix 8. 3 Interval Estimation with StatTools 346 Chapter 9 Hypothesis Tests 348 Statistics in Practice: John Morrell & Company 349 9. Developing Null and Alternative Hypotheses 350 The Alternative Hypothesis as a Research Hypothesis 350 The Null Hypothesis as an Assumption to Be Challenged 351 Summary of Forms for Null and Alternative Hypotheses 352 9. 2 Type I and Type II Errors 353 9. 3 Population Mean: Known 356 One-Tailed Test 356 Two-Tailed Test 362 Summary and Practical Advice 365 Contents xv Relationship Between Interval Estimation and Hypothesis Testing 366 9. 4 Population Mean: Unknown 370 One-Tailed Test 371 Two-Tailed Test 372 Summary and Practical Advice 373 9. 5 Population Proportion 376 Summary 379 9. 6 Hypothesis Testing and Decision Making 381 9. 7 Calculating the Probability of Type II Errors 382 9. Determining the Sample Size for a Hypothesis Test About a Population Mean 387 Summary 391 Glossary 392 Key Formulas 392 Supplementary Exercises 393 Case Problem 1: Quality Associates, Inc. 396 Case Problem 2: Ethical Behavior of Business Students at Bayview University 397 Appendix 9. 1 Hypothesis Testing with Minitab 398 Appendix 9. 2 Hypothesis Testing with Excel 400 Appendix 9. 3 Hypothesis Testing with StatTools 404 Chapter 10 Inference About Means and Proportions with Two Populations 406 Statistics in Practice: U. S. Food and Drug Administration 407 10. 1 Inferences About the Difference Between Two Population Means: 1 and 2 Known 408 Interval Estimation of 1 – 2 408 Hypothesis Tests About 1 – 2 410 Practical Advice 412 10. Inferences About the Difference Between Two Population Means: 1 and 2 Unknown 415 Interval Estimation of 1 – 2 415 Hypothesis Tests About 1 – 2 417 Practical Advice 419 10. 3 Inferences About the Difference Between Two Population Means: Matched Samples 423 10. 4 Inferences About the Difference Between Two Population Proportions 429 Interval Estimation of p1 – p2 429 Hypothesis Tests About p1 – p2 431 Summary 436 xvi Contents Glossary 436 Key Formulas 437 Supplementary Exercises 438 Case Problem: Par, Inc. 441 Appendix 10. 1 Inferences About Two Populations Using Minitab 442 Appendix 10. 2 Inferences About Two Populations Using Excel 444 Appendix 10. Inferences About Two Populations Using StatTools 446 Chapter 11 Inferences About Population Variances 448 Statistics in Practice: U. S. Government Accountability Office 449 11. 1 Inferences About a Population Variance 450 Interval Estimation 450 Hypothesis Testing 454 11. 2 Inferences About Two Population Variances 460 Summary 466 Key Formulas 467 Supplementary Exercises 467 Case Problem: Air Force Training Program 469 Appendix 11. 1 Population Variances with Minitab 470 Appendix 11. 2 Population Variances with Excel 470 Appendix 11. 3 Population Standard Deviation with StatTools 471 Chapter 12 Tests of Goodness of Fit and Independence 472 Statistics in Practice: United Way 473 12. Goodness of Fit Test: A Multinomial Population 474 12. 2 Test of Independence 479 12. 3 Goodness of Fit Test: Poisson and Normal Distributions 487 Poisson Distribution 487 Normal Distribution 491 Summary 496 Glossary 497 Key Formulas 497 Supplementary Exercises 497 Case Problem: A Bipartisan Agenda for Change 501 Appendix 12. 1 Tests of Goodness of Fit and Independence Using Minitab 502 Appendix 12. 2 Tests of Goodness of Fit and Independence Using Excel 503 Chapter 13 Experimental Design and Analysis of Variance 506 Statistics in Practice: Burke Marketing Services, Inc. 507 13. 1 An Introduction to Experimental Design and Analysis of Variance 508 Contents xvii
Data Collection 509 Assumptions for Analysis of Variance 510 Analysis of Variance: A Conceptual Overview 510 13. 2 Analysis of Variance and the Completely Randomized Design 513 Between-Treatments Estimate of Population Variance 514 Within-Treatments Estimate of Population Variance 515 Comparing the Variance Estimates: The F Test 516 ANOVA Table 518 Computer Results for Analysis of Variance 519 Testing for the Equality of k Population Means:An Observational Study 520 13. 3 Multiple Comparison Procedures 524 Fisher’s LSD 524 Type I Error Rates 527 13. 4 Randomized Block Design 530 Air Traffic Controller Stress Test 531 ANOVA Procedure 532 Computations and Conclusions 533 13. Factorial Experiment 537 ANOVA Procedure 539 Computations and Conclusions 539 Summary 544 Glossary 545 Key Formulas 545 Supplementary Exercises 547 Case Problem 1: Wentworth Medical Center 552 Case Problem 2: Compensation for Sales Professionals 553 Appendix 13. 1 Analysis of Variance with Minitab 554 Appendix 13. 2 Analysis of Variance with Excel 555 Appendix 13. 3 Analysis of Variance with StatTools 557 Chapter 14 Simple Linear Regression 560 Statistics in Practice: Alliance Data Systems 561 14. 1 Simple Linear Regression Model 562 Regression Model and Regression Equation 562 Estimated Regression Equation 563 14. 2 Least Squares Method 565 14. Coefficient of Determination 576 Correlation Coefficient 579 14. 4 Model Assumptions 583 14. 5 Testing for Significance 585 Estimate of 2 585 t Test 586 xviii Contents Confidence Interval for 1 587 F Test 588 Some Cautions About the Interpretation of Significance Tests 590 14. 6 Using the Estimated Regression Equation for Estimation and Prediction 594 Point Estimation 594 Interval Estimation 594 Confidence Interval for the Mean Value of y 595 Prediction Interval for an Individual Value of y 596 14. 7 Computer Solution 600 14. 8 Residual Analysis: Validating Model Assumptions 605 Residual Plot Against x 606 Residual Plot Against y 607 ? Standardized Residuals 607 Normal Probability Plot 610 14. Residual Analysis: Outliers and Influential Observations 614 Detecting Outliers 614 Detecting Influential Observations 616 Summary 621 Glossary 622 Key Formulas 623 Supplementary Exercises 625 Case Problem 1: Measuring Stock Market Risk 631 Case Problem 2: U. S. Department of Transportation 632 Case Problem 3: Alumni Giving 633 Case Problem 4: PGA Tour Statistics 633 Appendix 14. 1 Calculus-Based Derivation of Least Squares Formulas 635 Appendix 14. 2 A Test for Significance Using Correlation 636 Appendix 14. 3 Regression Analysis with Minitab 637 Appendix 14. 4 Regression Analysis with Excel 638 Appendix 14. 5 Regression Analysis with StatTools 640 Chapter 15 Multiple Regression 642 Statistics in Practice: dunnhumby 643 15. 1 Multiple Regression Model 644 Regression Model and Regression Equation 644 Estimated Multiple Regression Equation 644 15. Least Squares Method 645 An Example: Butler Trucking Company 646 Note on Interpretation of Coefficients 648 15. 3 Multiple Coefficient of Determination 654 15. 4 Model Assumptions 657 Contents xix 15. 5 Testing for Significance 658 F Test 658 t Test 661 Multicollinearity 662 15. 6 Using the Estimated Regression Equation for Estimation and Prediction 665 15. 7 Categorical Independent Variables 668 An Example: Johnson Filtration, Inc. 668 Interpreting the Parameters 670 More Complex Categorical Variables 672 15. 8 Residual Analysis 676 Detecting Outliers 678 Studentized Deleted Residuals and Outliers 678 Influential Observations 679 Using Cook’s Distance Measure to Identify Influential Observations 679 15. Logistic Regression 683 Logistic Regression Equation 684 Estimating the Logistic Regression Equation 685 Testing for Significance 687 Managerial Use 688 Interpreting the Logistic Regression Equation 688 Logit Transformation 691 Summary 694 Glossary 695 Key Formulas 696 Supplementary Exercises 698 Case Problem 1: Consumer Research, Inc. 704 Case Problem 2: Alumni Giving 705 Case Problem 3: PGA Tour Statistics 705 Case Problem 4: Predicting Winning Percentage for the NFL 708 Appendix 15. 1 Multiple Regression with Minitab 708 Appendix 15. 2 Multiple Regression with Excel 709 Appendix 15. 3 Logistic Regression with Minitab 710 Appendix 15. 4 Multiple Regression with StatTools 711
Chapter 16 Regression Analysis: Model Building 712 Statistics in Practice: Monsanto Company 713 16. 1 General Linear Model 714 Modeling Curvilinear Relationships 714 Interaction 718 xx Contents Transformations Involving the Dependent Variable 720 Nonlinear Models That Are Intrinsically Linear 724 16. 2 Determining When to Add or Delete Variables 729 General Case 730 Use of p-Values 732 16. 3 Analysis of a Larger Problem 735 16. 4 Variable Selection Procedures 739 Stepwise Regression 739 Forward Selection 740 Backward Elimination 741 Best-Subsets Regression 741 Making the Final Choice 742 16. 5 Multiple Regression Approach to Experimental Design 745 16. Autocorrelation and the Durbin-Watson Test 750 Summary 754 Glossary 754 Key Formulas 754 Supplementary Exercises 755 Case Problem 1: Analysis of PGA Tour Statistics 758 Case Problem 2: Fuel Economy for Cars 759 Appendix 16. 1 Variable Selection Procedures with Minitab 760 Appendix 16. 2 Variable Selection Procedures with StatTools 761 Chapter 17 Index Numbers 763 Statistics in Practice: U. S. Department of Labor, Bureau of Labor Statistics 764 17. 1 Price Relatives 765 17. 2 Aggregate Price Indexes 765 17. 3 Computing an Aggregate Price Index from Price Relatives 769 17. 4 Some Important Price Indexes 771 Consumer Price Index 771 Producer Price Index 771 Dow Jones Averages 772 17. 5 Deflating a Series by Price Indexes 773 17. 6 Price Indexes: Other Considerations 777 Selection of Items 777 Selection of a Base Period 777 Quality Changes 777 17. Quantity Indexes 778 Summary 780 Contents xxi Glossary 780 Key Formulas 780 Supplementary Exercises 781 Chapter 18 Time Series Analysis and Forecasting 784 Statistics in Practice: Nevada Occupational Health Clinic 785 18. 1 Time Series Patterns 786 Horizontal Pattern 786 Trend Pattern 788 Seasonal Pattern 788 Trend and Seasonal Pattern 789 Cyclical Pattern 789 Selecting a Forecasting Method 791 18. 2 Forecast Accuracy 792 18. 3 Moving Averages and Exponential Smoothing 797 Moving Averages 797 Weighted Moving Averages 800 Exponential Smoothing 800 18. 4 Trend Projection 807 Linear Trend Regression 807 Holt’s Linear Exponential Smoothing 812 Nonlinear Trend Regression 814 18. Seasonality and Trend 820 Seasonality Without Trend 820 Seasonality and Trend 823 Models Based on Monthly Data 825 18. 6 Time Series Decomposition 829 Calculating the Seasonal Indexes 830 Deseasonalizing the Time Series 834 Using the Deseasonalized Time Series to Identify Trend 834 Seasonal Adjustments 836 Models Based on Monthly Data 837 Cyclical Component 837 Summary 839 Glossary 840 Key Formulas 841 Supplementary Exercises 842 Case Problem 1: Forecasting Food and Beverage Sales 846 Case Problem 2: Forecasting Lost Sales 847 Appendix 18. 1 Forecasting with Minitab 848 Appendix 18. 2 Forecasting with Excel 851 Appendix 18. 3 Forecasting with StatTools 852 xxii Contents Chapter 19 Nonparametric Methods 855 Statistics in Practice: West Shell Realtors 856 19. Sign Test 857 Hypothesis Test About a Population Median 857 Hypothesis Test with Matched Samples 862 19. 2 Wilcoxon Signed-Rank Test 865 19. 3 Mann-Whitney-Wilcoxon Test 871 19. 4 Kruskal-Wallis Test 882 19. 5 Rank Correlation 887 Summary 891 Glossary 892 Key Formulas 893 Supplementary Exercises 893 Appendix 19. 1 Nonparametric Methods with Minitab 896 Appendix 19. 2 Nonparametric Methods with Excel 899 Appendix 19. 3 Nonparametric Methods with StatTools 901 Chapter 20 Statistical Methods for Quality Control 903 Statistics in Practice: Dow Chemical Company 904 20. 1 Philosophies and Frameworks 905 Malcolm Baldrige National Quality Award 906 ISO 9000 906 Six Sigma 906 20. Statistical Process Control 908 Control Charts 909 _ x Chart: Process Mean and Standard Deviation Known 910 _ x Chart: Process Mean and Standard Deviation Unknown 912 R Chart 915 p Chart 917 np Chart 919 Interpretation of Control Charts 920 20. 3 Acceptance Sampling 922 KALI, Inc. : An Example of Acceptance Sampling 924 Computing the Probability of Accepting a Lot 924 Selecting an Acceptance Sampling Plan 928 Multiple Sampling Plans 930 Summary 931 Glossary 931 Key Formulas 932 Supplementary Exercises 933 Appendix 20. 1 Control Charts with Minitab 935 Appendix 20. 2 Control Charts with StatTools 935 Contents xxiii Chapter 21 Decision Analysis 937 Statistics in Practice: Ohio Edison Company 938 21. Problem Formulation 939 Payoff Tables 940 Decision Trees 940 21. 2 Decision Making with Probabilities 941 Expected Value Approach 941 Expected Value of Perfect Information 943 21. 3 Decision Analysis with Sample Information 949 Decision Tree 950 Decision Strategy 951 Expected Value of Sample Information 954 21. 4 Computing Branch Probabilities Using Bayes’ Theorem 960 Summary 964 Glossary 965 Key Formulas 966 Supplementary Exercises 966 Case Problem: Lawsuit Defense Strategy 969 Appendix: An Introduction to PrecisionTree 970 Chapter 22 Sample Survey On Website Statistics in Practice: Duke Energy 22-2 22. 1 Terminology Used in Sample Surveys 22-2 22. 2 Types of Surveys and Sampling Methods 22-3 22. Survey Errors 22-5 Nonsampling Error 22-5 Sampling Error 22-5 22. 4 Simple Random Sampling 22-6 Population Mean 22-6 Population Total 22-7 Population Proportion 22-8 Determining the Sample Size 22-9 22. 5 Stratified Simple Random Sampling 22-12 Population Mean 22-12 Population Total 22-14 Population Proportion 22-15 Determining the Sample Size 22-16 22. 6 Cluster Sampling 22-21 Population Mean 22-23 Population Total 22-24 Population Proportion 22-25 Determining the Sample Size 22-26 22. 7 Systematic Sampling 22-29 Summary 22-29 xxiv Contents Glossary 22-30 Key Formulas 22-30 Supplementary Exercises 22-34 Appendix: Self-Test Solutions and Answers to Even-Numbered Exercises 22-37
Appendix A References and Bibliography 976 Appendix B Tables 978 Appendix C Summation Notation 1005 Appendix D Self-Test Solutions and Answers to Even-Numbered Exercises 1007 Appendix E Using Excel Functions 1062 Appendix F Computing p-Values Using Minitab and Excel 1067 Index 1071 Preface The purpose of STATISTICS FOR BUSINESS AND ECONOMICS 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 application setting, with the statistical results providing insights to decisions and solutions to problems. Although the book is applications oriented, we have taken care to provide sound methodological development and to use notation that is generally accepted for the topic being covered. Hence, students will find that this text provides good preparation for the study of more advanced statistical material. A bibliography to guide further study is included as an appendix.
The text introduces the student to the software packages of Minitab 15 and Microsoft® Office Excel 2007 and emphasizes the role of computer software in the application of statistical analysis. Minitab is illustrated as it is one of the leading statistical software packages for both education and statistical practice. Excel is not a statistical software package, but the wide availability and use of Excel make it important for students to understand the statistical capabilities of this package. Minitab and Excel procedures are provided in appendixes so that instructors have the flexibility of using as much computer emphasis as desired for the course.
Changes in the Eleventh Edition We appreciate the acceptance and positive response to the previous editions of STATISTICS FOR BUSINESS AND ECONOMICS. Accordingly, in making modifications for this new edition, we have maintained the presentation style and readability of those editions. The significant changes in the new edition are summarized here. Content Revisions • Revised Chapter 18 — “Time Series Analysis and Forecasting. ” The chapter has been completely rewritten to focus more on using the pattern in a time series plot to select an appropriate forecasting method. We begin with a new Section 18. 1 on time series patterns, followed by a new Section 18. on methods for measuring forecast accuracy. Section 18. 3 discusses moving averages and exponential smoothing. Section 18. 4 introduces methods appropriate for a time series that exhibits a trend. Here we illustrate how regression analysis and Holt’s linear exponential smoothing can be used for linear trend projection, and then discuss how regression analysis can be used to model nonlinear relationships involving a quadratic trend and an exponential growth. Section 18. 5 then shows how dummy variables can be used to model seasonality in a forecasting equation. Section 18. 6 discusses classical time series decomposition, including the concept of deseasonalizing a time series.
There is a new appendix on forecasting using the Excel add-in StatTools and most exercises are new or updated. • Revised Chapter 19 — “Nonparametric Methods. ” The treatment of nonparametric methods has been revised and updated. We contrast each nonparametric method xxvi Preface • • • • • • • • with its parametric counterpart and describe how fewer assumptions are required for the nonparametric procedure. The sign test emphasizes the test for a population median, which is important in skewed populations where the median is often the preferred measure of central location. The Wilcoxon Rank-Sum test is used for both matched samples tests and tests about a median of a symmetric population.
A new small-sample application of the Mann-Whitney-Wilcoxon test shows the exact sampling distribution of the test statistic and is used to explain why the sum of the signed ranks can be used to test the hypothesis that the two populations are identical. The chapter concludes with the Kruskal-Wallis test and rank correlation. New chapter ending appendixes describe how Minitab, Excel, and StatTools can be used to implement nonparametric methods. Twenty-seven data sets are now available to facilitate computer solution of the exercises. StatTools Add-In for Excel. Excel 2007 does not contain statistical functions or data analysis tools to perform all the statistical procedures discussed in the text.
StatTools is a commercial Excel 2007 add-in, developed by Palisades Corporation, that extends the range of statistical options for Excel users. In an appendix to Chapter 1 we show how to download and install StatTools, and most chapters include a chapter appendix that shows the steps required to accomplish a statistical procedure using StatTools. We have been very careful to make the use of StatTools completely optional so that instructors who want to teach using the standard tools available in Excel 2007 can continue to do so. But users who want additional statistical capabilities not available in standard Excel 2007 now have access to an industry standard statistics add-in that students will be able to continue to use in the workplace. Change in Terminology for Data.
In the previous edition, nominal and ordinal data were classified as qualitative; interval and ratio data were classified as quantitative. In this edition, nominal and ordinal data are referred to as categorical data. Nominal and ordinal data use labels or names to identify categories of like items. Thus, we believe that the term categorical is more descriptive of this type of data. Introducing Data Mining. A new section in Chapter 1 introduces the relatively new field of data mining. We provide a brief overview of data mining and the concept of a data warehouse. We also describe how the fields of statistics and computer science join to make data mining operational and valuable. Ethical Issues in Statistics.
Another new section in Chapter 1 provides a discussion of ethical issues when presenting and interpreting statistical information. Updated Excel Appendix for Tabular and Graphical Descriptive Statistics. The chapter-ending Excel appendix for Chapter 2 shows how the Chart Tools, PivotTable Report, and PivotChart Report can be used to enhance the capabilities for displaying tabular and graphical descriptive statistics. Comparative Analysis with Box Plots. The treatment of box plots in Chapter 2 has been expanded to include relatively quick and easy comparisons of two or more data sets. Typical starting salary data for accounting, finance, management, and marketing majors are used to illustrate box plot multigroup comparisons. Revised Sampling Material.
The introduction of Chapter 7 has been revised and now includes the concepts of a sampled population and a frame. The distinction between sampling from a finite population and an infinite population has been clarified, with sampling from a process used to illustrate the selection of a random sample from an infinite population. A practical advice section stresses the importance of obtaining close correspondence between the sampled population and the target population. Revised Introduction to Hypothesis Testing. Section 9. 1, Developing Null and Alternative Hypotheses, has been revised. A better set of guidelines has been developed for identifying the null and alternative hypotheses.
The context of the situation and the purpose for taking the sample are key. In situations in which the Preface xxvii • • • • focus is on finding evidence to support a research finding, the research hypothesis is the alternative hypothesis. In situations where the focus is on challenging an assumption, the assumption is the null hypothesis. New PrecisionTree Software for Decision Analysis. PrecisionTree is another Excel add-in developed by Palisades Corporation that is very helpful in decision analysis. Chapter 21 has a new appendix which shows how to use the PrecisionTree add-in. New Case Problems. We have added 5 new case problems to this edition, bringing the total number of case problems to 31.
A new case problem on descriptive statistics appears in Chapter 3 and a new case problem on hypothesis testing appears in Chapter 9. Three new case problems have been added to regression in Chapters 14, 15, and 16. These case problems provide students with the opportunity to analyze larger data sets and prepare managerial reports based on the results of the analysis. New Statistics in Practice Applications. Each chapter begins with a Statistics in Practice vignette that describes an application of the statistical methodology to be covered in the chapter. New to this edition are Statistics in Practice articles for Oceanwide Seafood in Chapter 4 and the London-based marketing services company dunnhumby in Chapter 15. New Examples and Exercises Based on Real Data.
We continue to make a significant effort to update our text examples and exercises with the most current real data and referenced sources of statistical information. In this edition, we have added approximately 150 new examples and exercises based on real data and referenced sources. Using data from sources also used by The Wall Street Journal, USA Today, Barron’s, and others, we have drawn from actual studies to develop explanations and to create exercises that demonstrate the many uses of statistics in business and economics. We believe that the use of real data helps generate more student interest in the material and enables the student to learn about both the statistical methodology and its application. The eleventh edition of the text contains over 350 examples and exercises based on real data.
Features and Pedagogy Authors Anderson, Sweeney, and Williams 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. Self-Test Exercises
Certain exercises are identified as “Self-Test Exercises. ” Completely worked-out solutions for these exercises are provided in Appendix D at the back of the book. Students can attempt the Self-Test Exercises and immediately check the solution to evaluate their understanding of the concepts presented in the chapter. 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. xxviii Preface
At the end of many sections, we provide Notes and Comments designed to give the student additional insights about the statistical methodology and its application. Notes and Comments include warnings about or limitations of the methodology, recommendations for application, brief descriptions of additional technical considerations, and other matters. Data Files Accompany the Text Over 200 data files are available on the website that accompanies the text. The data sets are available in both Minitab and Excel formats. File 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. Acknowledgments A special thank you goes to Jeffrey D. Camm, University of Cincinnati, and James J.
Cochran, Louisiana Tech University, for their contributions to this eleventh edition of Statistics for Business and Economics. Professors Camm and Cochran provided extensive input for the new chapters on forecasting and nonparametric methods. In addition, they provided helpful input and suggestions for new case problems, exercises, and Statistics in Practice articles. We would also like to thank 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. Finally, we are also indebted to our senior acquisitions editor Charles McCormick, Jr. , our developmental editor Maggie Kubale, our content project manager, Jacquelyn K Featherly, our marketing manager Bryant T.
Chrzan, and others at Cengage South-Western for their editorial counsel and support during the preparation of this text. David R. Anderson Dennis J. Sweeney Thomas A. Williams About the Authors David R. Anderson. David R. Anderson is Professor of Quantitative Analysis in the College of Business Administration at the University of Cincinnati. Born in Grand Forks, North Dakota, he earned his B. S. , M. S. , and Ph. D. degrees from Purdue University. Professor Anderson has served as Head of the Department of Quantitative Analysis and Operations Management and as Associate Dean of the College of Business Administration at the University of Cincinnati. In addition, he was the coordinator of the College’s first Executive Program.
At the University of Cincinnati, Professor Anderson has taught introductory statistics for business students as well as graduate-level courses in regression analysis, multivariate analysis, and management science. He has also taught statistical courses at the Department of Labor in Washington, D. C. He has been honored with nominations and awards for excellence in teaching and excellence in service to student organizations. Professor Anderson has coauthored 10 textbooks in the areas of statistics, management science, linear programming, and production and operations management. He is an active consultant in the field of sampling and statistical methods. Dennis J.
Sweeney. Dennis J. Sweeney is Professor of Quantitative Analysis and Founder of the Center for Productivity Improvement at the University of Cincinnati. Born in Des Moines, Iowa, he earned a B. S. B. A. degree from Drake University and his M. B. A. and D. B. A. degrees from Indiana University, where he was an NDEA Fellow. During 1978–79, Professor Sweeney worked in the management science group at Procter & Gamble; during 1981–82, he was 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 Cincinnati Gas & Electric have funded his research, which has been published in Management Science, Operations Research, Mathematical Programming, Decision Sciences, and other journals. Professor Sweeney has coauthored 10 textbooks in the areas of statistics, management science, linear programming, and production and operations management. Thomas A. Williams. Thomas A. Williams is Professor 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 teaches courses in management science and statistics, as well as graduate courses in regression and decision analysis.
Professor Williams is the coauthor of 11 textbooks in the areas of management 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. This page intentionally left blank STATISTICS FOR BUSINESS AND ECONOMICS 11e This page intentionally left blank CHAPTER Data and Statistics CONTENTS STATISTICS IN PRACTICE: BUSINESSWEEK 1. 1 APPLICATIONS IN BUSINESS AND ECONOMICS Accounting Finance Marketing Production Economics DATA Elements, Variables, and Observations Scales of Measurement Categorical and Quantitative Data Cross-Sectional and Time Series Data 1. DATA SOURCES Existing Sources Statistical Studies Data Acquisition Errors DESCRIPTIVE STATISTICS STATISTICAL INFERENCE COMPUTERS AND STATISTICAL ANALYSIS DATA MINING ETHICAL GUIDELINES FOR STATISTICAL PRACTICE 1 1. 4 1. 5 1. 6 1. 7 1. 8 1. 2 2 Chapter 1 Data and Statistics STATISTICS in PRACTICE NEW YORK, NEW YORK BUSINESSWEEK* With a global circulation of more than 1 million, BusinessWeek is the most widely read business magazine in the world. More than 200 dedicated reporters and editors in 26 bureaus worldwide deliver a variety of articles of interest to the business and economic community. Along with feature articles on current topics, the magazine contains regular sections on International Business, Economic Analysis, Information Processing, and Science & 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 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. For example, the February 23, 2009 issue contained a feature article about the home foreclosure crisis, the March 17, 2009 issue included a discussion of when the stock market would begin to recover, and the May 4, 2009 issue had a special report on how to make pay cuts less painful.
In addition, the weekly BusinessWeek Investor provides statistics about the state of the economy, including production indexes, stock prices, mutual funds, and interest rates. 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. BusinessWeek managers use statistical summaries from the survey to provide better services to subscribers and advertisers. One recent North *The authors are indebted to Charlene Trentham, Research Manager at BusinessWeek, for providing this Statistics in Practice. BusinessWeek uses statistical facts and summaries in many of its articles. © Terri Miller/E-Visual Communications, Inc.
American subscriber survey indicated that 90% of BusinessWeek subscribers use a personal computer at home and that 64% of BusinessWeek subscribers are involved with computer purchases at work. Such statistics alert BusinessWeek managers to subscriber interest in articles about new developments in computers. The results of the survey are also made available to potential advertisers. The high percentage of subscribers using personal computers at home and the high percentage of subscribers involved with computer purchases at work would be an incentive for a computer manufacturer to consider advertising in 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. Frequently, we see the following types of statements in newspapers and magazines: • The National Association of Realtors reported that the median price paid by firsttime home buyers is $165,000 (The Wall Street Journal, February 11, 2009). • NCAA president Myles Brand reported that college athletes are earning degrees at record rates. Latest figures show that 79% of all men and women student-athletes graduate (Associated Press, October 15, 2008). • The average one-way travel time to work is 25. 3 minutes (U. S. Census Bureau, March 2009). 1. 1 Applications in Business and Economics 3 • A record high 11% of U. S. omes are vacant, a glut created by the housing boom and subsequent collapse (USA Today, February 13, 2009). • The national average price for regular gasoline reached $4. 00 per gallon for the first time in history (Cable News Network website, June 8, 2008). • The New York Yankees have the highest salaries in major league baseball. The total payroll is $201,449,289 with a median salary of $5,000,000 (USA Today Salary Data Base, April 2009). • The Dow Jones Industrial Average closed at 8721 (The Wall Street Journal, June 2, 2009). The numerical facts in the preceding statements ($165,000, 79%, 25. 3, 11%, $4. 00, $201,449,289, $5,000,000 and 8721) are called statistics.
In this usage, the term statistics refers to numerical facts such as averages, medians, percents, and index numbers that help us understand a variety of business and economic situations. However, as you will see, the field, or subject, of statistics involves much more than numerical facts. In a broader sense, statistics is defined as 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 important role that the Internet now plays in obtaining data is also highlighted. The uses of data in developing descriptive statistics and in making statistical inferences are described in Sections 1. 4 and 1. 5.
The last three sections of Chapter 1 provide the role of the computer in statistical analysis, an introduction to the relative new field of data mining, and a discussion of ethical guidelines for statistical practice. A chapter-ending appendix includes an introduction to the add-in StatTools which can be used to extend the statistical options for users of Microsoft Excel. 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. 4 Chapter 1 Data and Statistics Finance Financial analysts use a variety of statistical information to guide their investment recommendations.
In the case of stocks, the analysts review a variety of financial data including price/earnings ratios and dividend yields. By comparing the information for an individual stock with information about the stock market averages, a financial analyst can begin to draw a conclusion as to whether an individual stock is over- or underpriced. For example, Barron’s (February 18, 2008) reported that the average dividend yield for the 30 stocks in the Dow Jones Industrial Average was 2. 45%. Altria Group showed a dividend yield of 3. 05%. In this case, the statistical information on dividend yield indicates a higher dividend yield for Altria Group than the average for the Dow Jones stocks. Therefore, a financial analyst might conclude that Altria Group was underpriced.
This and other information about Altria Group would help the analyst make a buy, sell, or hold recommendation for the stock. Marketing Electronic scanners at retail checkout counters collect data for a variety of marketing research applications. For example, data suppliers such as ACNielsen and Information Resources, Inc. , 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. 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. 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 25 mutual funds that are part of the Morningstar Funds500 for 2008. Morningstar is a company that tracks over 7000 mutual funds and prepares in-depth analyses of 2000 of these. Their recommendations are followed closely by financial analysts and individual investors. Elements, Variables, and Observations Elements are the entities on which data are collected.
For the data set in Table 1. 1 each individual mutual fund is an element: the element names appear in the first column. With 25 mutual funds, the data set contains 25 elements. A variable is a characteristic of interest for the elements. The data set in Table 1. 1 includes the following five variables: • Fund Type: The type of mutual fund, labeled DE (Domestic Equity), IE (International Equity), and FI (Fixed Income) • Net Asset Value ($): The closing price per share on December 31, 2007 TABLE 1. 1 DATA SET FOR 25 MUTUAL FUNDS 5-Year Expense Net Asset Average Ratio Morningstar Value ($) Return (%) (%) Rank 14. 37 10. 73 24. 94 16. 92 35. 73 13. 47 73. 1 48. 39 45. 60 8. 60 49. 81 15. 30 17. 44 27. 86 40. 37 10. 68 26. 27 53. 89 22. 46 37. 53 12. 10 24. 42 15. 68 32. 58 35. 41 30. 53 3. 34 10. 88 15. 67 15. 85 17. 23 17. 99 23. 46 13. 50 2. 76 16. 70 15. 31 15. 16 32. 70 9. 51 13. 57 23. 68 51. 10 16. 91 15. 46 4. 31 13. 41 2. 37 17. 01 13. 98 1. 41 0. 49 0. 99 1. 18 1. 20 0. 53 0. 89 0. 90 0. 89 0. 45 1. 36 1. 32 1. 31 1. 16 1. 05 1. 25 1. 36 1. 24 0. 80 1. 27 0. 62 0. 29 0. 16 0. 23 1. 19 3-Star 4-Star 3-Star 3-Star 4-Star 3-Star 5-Star 4-Star 3-Star 3-Star 4-Star 3-Star 5-Star 3-Star 2-Star 3-Star 4-Star 4-Star 4-Star 4-Star 3-Star 4-Star 3-Star 3-Star 4-Star Fund Name American Century Intl.
Disc American Century Tax-Free Bond American Century Ultra Artisan Small Cap Brown Cap Small DFA U. S. Micro Cap Fidelity Contrafund Fidelity Overseas Fidelity Sel Electronics Fidelity Sh-Term Bond Gabelli Asset AAA Kalmar Gr Val Sm Cp Marsico 21st Century Mathews Pacific Tiger Oakmark I PIMCO Emerg Mkts Bd D RS Value A T. Rowe Price Latin Am. T. Rowe Price Mid Val Thornburg Value A USAA Income Vanguard Equity-Inc Vanguard Sht-Tm TE Vanguard Sm Cp Idx Wasatch Sm Cp Growth Fund Type IE FI DE DE DE DE DE IE DE FI DE DE DE IE DE FI DE IE DE DE FI DE FI DE DE WEB file Morningstar Data sets such as Morningstar are available on the website for this text. Source: Morningstar Funds500 (2008). 6 Chapter 1
Data and Statistics • 5-Year Average Return (%): The average annual return for the fund over the past 5 years • Expense Ratio: The percentage of assets deducted each fiscal year for fund expenses • Morningstar Rank: The overall risk-adjusted star rating for each fund; Morningstar ranks go from a low of 1-Star to a high of 5-Stars 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 set of measurements for the first observation (American Century Intl. Disc) is IE, 14. 37, 30. 53, 1. 41, and 3-Star.
The set of measurements for the second observation (American Century Tax-Free Bond) is FI, 10. 73, 3. 34, 0. 49, and 4-Star, and so on. A data set with 25 elements contains 25 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. , we see that the scale of measurement for the Fund Type variable is nominal because DE, IE, and FI are labels used to identify the category or type of fund. In cases where the scale of measurement is nominal, a numeric code as well as nonnumeric labels may be used. For example, to facilitate data collection and to prepare the data for entry into a computer database, we might use a numeric code by letting 1 denote Domestic Equity, 2 deno

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