Statistics for business economics by anderson PDF

Preview

Summary

CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Entries in this table give the area under the curve to the left of the Cumulative z value. For example, for probability z = –.85, the cumulative probability is .1977. z 0 z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 !3.0 .0013 .0013 .0013 ....

Description

CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION

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.

Cumulative probability

z

0

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

!3.0

.0013

.0013

.0013

.0012

.0012

.0011

.0011

.0011

.0010

.0010

!2.9 !2.8 !2.7 !2.6 !2.5

.0019 .0026 .0035 .0047 .0062

.0018 .0025 .0034 .0045 .0060

.0018 .0024 .0033 .0044 .0059

.0017 .0023 .0032 .0043 .0057

.0016 .0023 .0031 .0041 .0055

.0016 .0022 .0030 .0040 .0054

.0015 .0021 .0029 .0039 .0052

.0015 .0021 .0028 .0038 .0051

.0014 .0020 .0027 .0037 .0049

.0014 .0019 .0026 .0036 .0048

!2.4 !2.3 !2.2 !2.1 !2.0

.0082 .0107 .0139 .0179 .0228

.0080 .0104 .0136 .0174 .0222

.0078 .0102 .0132 .0170 .0217

.0075 .0099 .0129 .0166 .0212

.0073 .0096 .0125 .0162 .0207

.0071 .0094 .0122 .0158 .0202

.0069 .0091 .0119 .0154 .0197

.0068 .0089 .0116 .0150 .0192

.0066 .0087 .0113 .0146 .0188

.0064 .0084 .0110 .0143 .0183

!1.9 !1.8 !1.7 !1.6 !1.5

.0287 .0359 .0446 .0548 .0668

.0281 .0351 .0436 .0537 .0655

.0274 .0344 .0427 .0526 .0643

.0268 .0336 .0418 .0516 .0630

.0262 .0329 .0409 .0505 .0618

.0256 .0322 .0401 .0495 .0606

.0250 .0314 .0392 .0485 .0594

.0244 .0307 .0384 .0475 .0582

.0239 .0301 .0375 .0465 .0571

.0233 .0294 .0367 .0455 .0559

!1.4 !1.3 !1.2 !1.1 !1.0

.0808 .0968 .1151 .1357 .1587

.0793 .0951 .1131 .1335 .1562

.0778 .0934 .1112 .1314 .1539

.0764 .0918 .1093 .1292 .1515

.0749 .0901 .1075 .1271 .1492

.0735 .0885 .1056 .1251 .1469

.0721 .0869 .1038 .1230 .1446

.0708 .0853 .1020 .1210 .1423

.0694 .0838 .1003 .1190 .1401

.0681 .0823 .0985 .1170 .1379

!.9 !.8 !.7 !.6 !.5

.1841 .2119 .2420 .2743 .3085

.1814 .2090 .2389 .2709 .3050

.1788 .2061 .2358 .2676 .3015

.1762 .2033 .2327 .2643 .2981

.1736 .2005 .2296 .2611 .2946

.1711 .1977 .2266 .2578 .2912

.1685 .1949 .2236 .2546 .2877

.1660 .1922 .2206 .2514 .2843

.1635 .1894 .2177 .2483 .2810

.1611 .1867 .2148 .2451 .2776

!.4 !.3 !.2 !.1 !.0

.3446 .3821 .4207 .4602 .5000

.3409 .3783 .4168 .4562 .4960

.3372 .3745 .4129 .4522 .4920

.3336 .3707 .4090 .4483 .4880

.3300 .3669 .4052 .4443 .4840

.3264 .3632 .4013 .4404 .4801

.3228 .3594 .3974 .4364 .4761

.3192 .3557 .3936 .4325 .4721

.3156 .3520 .3897 .4286 .4681

.3121 .3483 .3859 .4247 .4641

CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION

Cumulative probability

0

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.

z

z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

.0 .1 .2 .3 .4

.5000 .5398 .5793 .6179 .6554

.5040 .5438 .5832 .6217 .6591

.5080 .5478 .5871 .6255 .6628

.5120 .5517 .5910 .6293 .6664

.5160 .5557 .5948 .6331 .6700

.5199 .5596 .5987 .6368 .6736

.5239 .5636 .6026 .6406 .6772

.5279 .5675 .6064 .6443 .6808

.5319 .5714 .6103 .6480 .6844

.5359 .5753 .6141 .6517 .6879

.5 .6 .7 .8 .9

.6915 .7257 .7580 .7881 .8159

.6950 .7291 .7611 .7910 .8186

.6985 .7324 .7642 .7939 .8212

.7019 .7357 .7673 .7967 .8238

.7054 .7389 .7704 .7995 .8264

.7088 .7422 .7734 .8023 .8289

.7123 .7454 .7764 .8051 .8315

.7157 .7486 .7794 .8078 .8340

.7190 .7517 .7823 .8106 .8365

.7224 .7549 .7852 .8133 .8389

1.0 1.1 1.2 1.3 1.4

.8413 .8643 .8849 .9032 .9192

.8438 .8665 .8869 .9049 .9207

.8461 .8686 .8888 .9066 .9222

.8485 .8708 .8907 .9082 .9236

.8508 .8729 .8925 .9099 .9251

.8531 .8749 .8944 .9115 .9265

.8554 .8770 .8962 .9131 .9279

.8577 .8790 .8980 .9147 .9292

.8599 .8810 .8997 .9162 .9306

.8621 .8830 .9015 .9177 .9319

1.5 1.6 1.7 1.8 1.9

.9332 .9452 .9554 .9641 .9713

.9345 .9463 .9564 .9649 .9719

.9357 .9474 .9573 .9656 .9726

.9370 .9484 .9582 .9664 .9732

.9382 .9495 .9591 .9671 .9738

.9394 .9505 .9599 .9678 .9744

.9406 .9515 .9608 .9686 .9750

.9418 .9525 .9616 .9693 .9756

.9429 .9535 .9625 .9699 .9761

.9441 .9545 .9633 .9706 .9767

2.0 2.1 2.2 2.3 2.4

.9772 .9821 .9861 .9893 .9918

.9778 .9826 .9864 .9896 .9920

.9783 .9830 .9868 .9898 .9922

.9788 .9834 .9871 .9901 .9925

.9793 .9838 .9875 .9904 .9927

.9798 .9842 .9878 .9906 .9929

.9803 .9846 .9881 .9909 .9931

.9808 .9850 .9884 .9911 .9932

.9812 .9854 .9887 .9913 .9934

.9817 .9857 .9890 .9913 .9936

2.5 2.6 2.7 2.8 2.9

.9938 .9953 .9965 .9974 .9981

.9940 .9955 .9966 .9975 .9982

.9941 .9956 .9967 .9976 .9982

.9943 .9957 .9968 .9977 .9983

.9945 .9959 .9969 .9977 .9984

.9946 .9960 .9970 .9978 .9984

.9948 .9961 .9971 .9979 .9985

.9949 .9962 .9972 .9979 .9985

.9951 .9963 .9973 .9980 .9986

.9952 .9964 .9974 .9981 .9986

3.0

.9986

.9987

.9987

.9988

.9988

.9989

.9989

.9989

.9990

.9990

STATISTICS FOR BUSINESS AND ECONOMICS 10e

This page intentionally left blank

STATISTICS FOR BUSINESS AND ECONOMICS 10e David R. Anderson University of Cincinnati

Dennis J. Sweeney University of Cincinnati

Thomas A. Williams Rochester Institute of Technology

Statistics for Business and Economics, Tenth Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams

VP/Editorial Director: Jack W. Calhoun

Manager, Editorial Media: John Barans

Art Director: Stacy Jenkins Shirley

Editor-in-Chief: Alex von Rosenberg

Technology Project Manager: John Rich

Internal Designers: Michael Stratton/cmiller design

Senior Acquisitions Editor: Charles McCormick, Jr.

Senior Manufacturing Coordinator: Diane Gibbons

Cover Designer: Paul Neff

Senior Developmental Editor: Alice Denny

Production House: Interactive Composition Corporation

Cover Images: © Brand X Images/Getty Images

Senior Marketing Manager: Larry Qualls

Printer: RR Donnelley Willard Manufacturing Division

Photography Manager: John Hill

ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution or information storage and retrieval systems, or in any other manner—without the written permission of the publisher.

Library of Congress Control Number: 2006927620

Marketing Communications Manager: Libby Shipp

Photo Researcher: Darren Wright

Content Project Manager: Amy Hackett COPYRIGHT © 2008, 2005 Thomson South-Western, a part of The Thomson Corporation. Thomson, the Star logo, and South-Western are trademarks used herein under license. Printed in the United States of America 1 2 3 4 5 09 08 07 06 Student Edition: ISBN 13: 978-0-324-36505-4 ISBN 10: 0-324-36505-5 Student Edition with CD: ISBN 13: 978-0-324-36068-4 ISBN 10: 0-324-36068-1 Instructor’s Edition: ISBN 13: 978-0-324-36507-8 ISBN 10: 0-324-36507-1 Instructor’s Edition with CD: ISBN 13: 978-0-324-36509-2 ISBN 10: 0-324-36509-8

For permission to use material from this text or product, submit a request online at http://www.thomsonrights.com.

For more information about our products, contact us at: Thomson Learning Academic Resource Center 1-800-423-0563 Thomson Higher Education 5191 Natorp Boulevard Mason, OH 45040 USA

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 26 Chapter 3 Descriptive Statistics: Numerical Measures 81 Chapter 4 Introduction to Probability 141 Chapter 5 Discrete Probability Distributions 186 Chapter 6 Continuous Probability Distributions 225 Chapter 7 Sampling and Sampling Distributions 257 Chapter 8 Interval Estimation 299 Chapter 9 Hypothesis Tests 338 Chapter 10 Statistical Inference About Means and Proportions with Two Populations 393 Chapter 11 Inferences About Population Variances 434 Chapter 12 Tests of Goodness of Fit and Independence 457 Chapter 13 Experimental Design and Analysis of Variance 490 Chapter 14 Simple Linear Regression 543 Chapter 15 Multiple Regression 624 Chapter 16 Regression Analysis: Model Building 693 Chapter 17 Index Numbers 744 Chapter 18 Forecasting 765 Chapter 19 Nonparametric Methods 812 Chapter 20 Statistical Methods for Quality Control 846 Chapter 21 Decision Analysis 879 Chapter 22 Sample Survey On CD Appendix A References and Bibliography 916 Appendix B Tables 918 Appendix C Summation Notation 946 Appendix D Self-Test Solutions and Answers to Even-Numbered Exercises 948 Appendix E Using Excel Functions 995 Appendix F Computing p-Values Using Minitab and Excel 1000 Index 1004

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 1.2 Data 5 Elements, Variables, and Observations 6 Scales of Measurement 6 Qualitative 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 12 1.4 Descriptive Statistics 13 1.5 Statistical Inference 15 1.6 Computers and Statistical Analysis 17 Summary 17 Glossary 18 Supplementary Exercises 19

Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations 26

Statistics in Practice: Colgate-Palmolive Company 27 2.1 Summarizing Qualitative Data 28 Frequency Distribution 28 Relative Frequency and Percent Frequency Distributions 29 Bar Graphs and Pie Charts 29 2.2 Summarizing Quantitative Data 34 Frequency Distribution 34

x

Contents

Relative Frequency and Percent Frequency Distributions 35 Dot Plot 36 Histogram 36 Cumulative Distributions 37 Ogive 39 2.3 Exploratory Data Analysis: The Stem-and-Leaf Display 43 2.4 Crosstabulations and Scatter Diagrams 48 Crosstabulation 48 Simpson’s Paradox 51 Scatter Diagram and Trendline 52 Summary 57 Glossary 59 Key Formulas 60 Supplementary Exercises 60 Case Problem 1: Pelican Stores 66 Case Problem 2: Motion Picture Industry 67 Appendix 2.1 Using Minitab for Tabular and Graphical Presentations 68 Appendix 2.2 Using Excel for Tabular and Graphical Presentations 70

Chapter 3 Descriptive Statistics: Numerical Measures 81 Statistics in Practice: Small Fry Design 82 3.1 Measures of Location 83 Mean 83 Median 84 Mode 85 Percentiles 86 Quartiles 87 3.2 Measures of Variability 91 Range 92 Interquartile Range 92 Variance 93 Standard Deviation 95 Coefficient of Variation 95 3.3 Measures of Distribution Shape, Relative Location, and Detecting Outliers 98 Distribution Shape 98 z-Scores 99 Chebyshev’s Theorem 100 Empirical Rule 101 Detecting Outliers 102 3.4 Exploratory Data Analysis 105 Five-Number Summary 105 Box Plot 106

Contents

3.5 Measures of Association Between Two Variables 110 Covariance 110 Interpretation of the Covariance 112 Correlation Coefficient 114 Interpretation of the Correlation Coefficient 115 3.6 The Weighted Mean and Working with Grouped Data 119 Weighted Mean 119 Grouped Data 120 Summary 124 Glossary 125 Key Formulas 126 Supplementary Exercises 128 Case Problem 1: Pelican Stores 132 Case Problem 2: Motion Picture Industry 133 Case Problem 3: Business Schools of Asia-Pacific 133 Appendix 3.1 Descriptive Statistics Using Minitab 135 Appendix 3.2 Descriptive Statistics Using Excel 137

Chapter 4 Introduction to Probability 141 Statistics in Practice: Rohm and Hass Company 142 4.1 Experiments, Counting Rules, and Assigning Probabilities 143 Counting Rules, Combinations, and Permutations 144 Assigning Probabilities 148 Probabilities for the KP&L Project 150 4.2 Events and Their Probabilities 153 4.3 Some Basic Relationships of Probability 157 Complement of an Event 157 Addition Law 158 4.4 Conditional Probability 163 Independent Events 167 Multiplication Law 167 4.5 Bayes’ Theorem 171 Tabular Approach 175 Summary 177 Glossary 177 Key Formulas 178 Supplementary Exercises 179 Case Problem: Hamilton County Judges 183

xi

xii

Contents

Chapter 5 Discrete Probability Distributions 186 Statistics in Practice: Citibank 187 5.1 Random Variables 187 Discrete Random Variables 188 Continuous Random Variables 189 5.2 Discrete Probability Distributions 190 5.3 Expected Value and Variance 196 Expected Value 196 Variance 196 5.4 Binomial Probability Distribution 200 A Binomial Experiment 201 Martin Clothing Store Problem 202 Using Tables of Binomial Probabilities 206 Expected Value and Variance for the Binomial Distribution 207 5.5 Poisson Probability Distribution 210 An Example Involving Time Intervals 211 An Example Involving Length or Distance Intervals 213 5.6 Hypergeometric Probability Distribution 214 Summary 217 Glossary 218 Key Formulas 219 Supplementary Exercises 220 Appendix 5.1 Discrete Probability Distributions with Minitab 222 Appendix 5.2 Discrete Probability Distributions with Excel 223

Chapter 6 Continuous Probability Distributions 225 Statistics in Practice: Procter & Gamble 226 6.1 Uniform Probability Distribution 227 Area as a Measure of Probability 228 6.2 Normal Probability Distribution 231 Normal Curve 231 Standard Normal Probability Distribution 233 Computing Probabilities for Any Normal Probability Distribution 238 Grear Tire Company Problem 239 6.3 Normal Approximation of Binomial Probabilities 243 6.4 Exponential Probability Distribution 246 Computing Probabilities for the Exponential Distribution 247 Relationship Between the Poisson and Exponential Distributions 248 Summary 250 Glossary 250 Key Formulas 251 Supplementary Exercises 251

Contents

Case Problem: Specialty Toys 254 Appendix 6.1 Continuous Probability Distributions with Minitab 255 Appendix 6.2 Continuous Probability Distributions with Excel 256

Chapter 7 Sampling and Sampling Distributions 257 Statistics in Practice: MeadWestvaco Corporation 258 7.1 The Electronics Associates Sampling Problem 259 7.2 Simple Random Sampling 260 Sampling from a Finite Population 260 Sampling from an Infinite Population 261 7.3 Point Estimation 264 7.4 Introduction to Sampling Distributions 267 _ 7.5 Sampling Distribution of x 270 _ Expected Value of x 270 _ Standard Deviation of x 271 _ Form of the Sampling Distribution of x 272 _ Sampling Distribution of x for the EAI Problem 274 _ Practical Value of the Sampling Distribution of x 274 Relationship Between the Sample Size and the Sampling _ Distribution of x 276 _ 7.6 Sampling Distribution of p 280 _ Expected Value of p 280 _ Standard Deviation of p 281 _ Form of the Sampling Distribution of p 281 _ Practical Value of the Sampling Distribution of p 282 7.7 Properties of Point Estimators 285 Unbiased 286 Efficiency 287 Consistency 287 7.8 Other Sampling Methods 288 Stratified Random Sampling 288 Cluster Sampling 289 Systematic Sampling 289 Convenience Sampling 290 Judgment Sampling 290 Summary 291 Glossary 291 Key Formulas 292 Supplementary Exercises 292 _ Appendix 7.1 The Expected Value and Standard Deviation of x 295 Appendix 7.2 Random Sampling with Minitab 296 Appendix 7.3 Random Sampling with Excel 297

xiii

xiv

Contents

Chapter 8 Interval Estimation 299 Statistics in Practice: Food Lion 300 8.1 Population Mean: ! Known 301 Margin of Error and the Interval Estimate 301 Practical Advice 305 8.2 Population Mean: ! Unknown 307 Margin of Error and the Interval Estimate 308 Practical Advice 311 Using a Small Sample 311 Summary of Interval Estimation Procedures 313 8.3 Determining the Sample Size 316 8.4 Population Proportion 319 Determining the Sample Size 321 Summary 324 Glossary 325 Key Formulas 326 Supplementary Exercises 326 Case Problem 1: Young Professional Magazine 329 Case Problem 2: Gulf Real Estate Properties 330 Case Problem 3: Metropolitan Research, Inc. 332 Appendix 8.1 Interval Estimation with Minitab 332 Appendix 8.2 Interval Estimation Using Excel 334

Chapter 9 Hypothesis Tests 338 Statistics in Practice: John Morrell & Company 339 9.1 Developing Null and Alternative Hypotheses 340 Testing Research Hypotheses 340 Testing the Validity of a Claim 340 Testing in Decision-Making Situations 341 Summary of Forms for Null and Alternative Hypotheses 341 9.2 Type I and Type II Errors 342 9.3 Population Mean: ! Known 345 One-Tailed Test 345 Two-Tailed Test 351 Summary and Practical Advice 354 Relationship Between Interval Estimation and Hypothesis Testing 355 9.4 Population Mean: ! Unknown 359 One-Tailed Test 360 Two-Tailed Test 361 Summary and Practical Advice 362

xv

Contents

9.5 Population Proportion 365 Summary 368 9.6 Hypothesis Testing and Decision Making 370 9.7 Calculating the Probability of Type II Errors 371 9.8 Determining the Sample Size for a Hypothesis Test About a Population Mean 376 Summary 380 Glossary 381 Key Formulas 381 Supplementary Exercises 382 Case Problem 1: Quality Associates, Inc. 385 Case Problem 2: Unemployment Study 386 Appendix 9.1 Hypothesis Testing with Minitab 386 Appendix 9.2 Hypothesis Testing with Excel 388

Chapter 10 Statistical Inference About Means and Proportions with Two Populations 393

Statistics in Practice: U.S. Food and Drug Administration 394 10.1 Inferences About the Difference Between Two Population Means: !1 and !2 Known 395 Interval Estimation of "1 – "2 395 Hypothesis Tests About "1 – "2 397 Practical Advice 399 10.2 Inferences About the Difference Between Two Population Means: !1 and !2 Unknown 402 Interval Estimation of "1 – "2 402 Hypothesis Tests About "1 – "2 403 Practical Advice 406 10.3 Inferences About the Difference Between Two Population Means: Matched Samples 410 10.4 Inferences About the Difference Between Two Population Proportions 416 Interval Estimati...