Statistics for Economics, Accounting and Business Studies fourth edition Michael Barrow Additional student support at www.pearsoned.co.uk/barrow Additional student support at www.pearsoned.co.uk/barrow 9 780273 683087 ISBN 0-273-68308-X www.pearson-books.com An imprint of Statistics for Economics, Accounting and Business Studies Barrow fourth edition New to this edition: More worked examples and real life business applications show students how to use the various techniques Section exercises and end of chapter problems allow for practice and testing Chapters have been reorganised, making the order more logical and flexible Features: Assumes no prior knowledge of statistics or advanced level mathematics Numerous real-life examples, problems and applications are included, some based on Excel Use of computing in statistics is explained and illustrated using industry- based software, databases, etc. Boxes highlight interesting issues, common mistakes and give advice on using computers in statistical analysis A website accompanies the book with resources for students and instructors This fourth edition of Statistics for Economics, Accounting and Business Studies is written to provide a clear and concise introduction to a range of statistical concepts and techniques. Throughout the text the author highlights how and why these techniques can be used to solve real-life problems, ensuring that the material is relevant to the experience of the student. This is a core text for introductory courses in statistics at undergraduate and MBA level. The book will be particularly suitable for economics and accounting students and will also appeal to those taking courses in business studies. Michael Barrow is Senior Lecturer in Economics at the University of Sussex and has acted as a consultant for major industrial, commercial and governmental bodies. Statistics for Economics, Accounting and Business Studies fourth edition Michael Barrow ‘An excellent reference book for the undergraduate student; filled with examples and applications – both practical (i.e. computer based) and traditional (i.e. pen and paper problems); wide-ranging and sensibly ordered. The book is clearly written, easy to follow… yet not in the least patronising. This is a particular strength.’ Christopher Gerry, UCL Front cover image: © Getty Images 027368308X_COVER 3/23/07 12:29 PM Page 1 Statistics for Economics, Accounting and Business Studies Visit the Statistics for Economics, Accounting and Business Studies, fourth edition Companion Website at www.pearsoned.co.uk/barrow to find valuable student learning material including: n Additional explanation of some topics with further references n Excel worksheets and demonstrations n Annotated links to other useful websites SFE_A01.qxd 3/23/07 10:06 AM Page i We work with leading authors to develop the strongest educational materials in Accounting, bringing cutting-edge thinking and best learning practice to a global market. Under a range of well-known imprints, including Financial Times Prentice Hall, we craft high quality print and electronic publications which help readers to understand and apply their content, whether studying or at work. To find out more about the complete range of our publishing, please visit us on the World Wide Web at: www.pearsoned.co.uk SFE_A01.qxd 3/23/07 10:06 AM Page ii Fourth Edition Statistics for Economics, Accounting and Business Studies Michael Barrow University of Sussex SFE_A01.qxd 3/23/07 10:06 AM Page iii Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk First published 1988 Fourth edition published 2006 © Pearson Education Limited 1988, 2006 The right of Michael Barrow to be identified as author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. ISBN: 978-0-273-68308-7 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Barrow, Michael. Statistics for economics, accounting, and business studies / Michael Barrow.— 4th ed. p. cm. Includes index. ISBN-13: 978-0-273-68308-7 ISBN-10: 0-273-68308-X 1. Economics–—Statistical methods. 2. Commercial statistics. I. Title. HB137.B37 2006 519.5024'33—dc22 2005056640 109876543 10 09 08 07 06 Typeset in 9/12pt Stone Serif by 35 Printed and bound in Malaysia. The publisher’s policy is to use paper manufactured from sustainable forests. SFE_A01.qxd 3/23/07 10:06 AM Page iv For Patricia, Caroline and Nicolas SFE_A01.qxd 3/23/07 10:06 AM Page v SFE_A01.qxd 3/23/07 10:06 AM Page vi Contents Preface to the fourth edition xiii Introduction 1 1 Descriptive statistics 7 Learning outcomes 8 Introduction 8 Summarising data using graphical techniques 10 Looking at cross-section data: wealth in the UK in 2001 15 Summarising data using numerical techniques 23 The box and whiskers diagram 41 Time-series data: investment expenditures 1970–2002 42 Graphing bivariate data: the scatter diagram 55 Data transformations 57 Guidance to the student: how to measure your progress 59 Summary 59 Key terms and concepts 60 Problems 60 Reference 66 Answers to exercises 66 Appendix 1A: ΣΣ notation 70 Problems on ΣΣ notation 71 Appendix 1B: E and V operators 72 Appendix 1C: Using logarithms 73 Problems on logarithms 74 2 Probability 75 Learning outcomes 75 Probability theory and statistical inference 76 The definition of probability 76 Probability theory: the building blocks 78 Bayes’ theorem 86 Decision analysis 88 Summary 92 Key terms and concepts 93 Problems 93 Answers to exercises 98 SFE_A01.qxd 3/23/07 10:06 AM Page vii viii Contents 3 Probability distributions 101 Learning outcomes 101 Introduction 101 Random variables 102 The Binomial distribution 103 The Normal distribution 109 The sample mean as a Normally distributed variable 116 The relationship between the Binomial and Normal distributions 122 The Poisson distribution 123 Summary 126 Key terms and concepts 126 Problems 126 Answers to exercises 131 4 Estimation and confidence intervals 133 Learning outcomes 133 Introduction 134 Point and interval estimation 134 Rules and criteria for finding estimates 135 Estimation with large samples 138 Precisely what is a confidence interval? 141 Estimation with small samples: the t distribution 148 Summary 153 Key terms and concepts 154 Problems 154 Answers to exercises 156 Appendix: Derivations of sampling distributions 158 5 Hypothesis testing 159 Learning outcomes 159 Introduction 160 The concepts of hypothesis testing 160 The Prob-value approach 167 Significance, effect size and power 168 Further hypothesis tests 169 Hypothesis tests with small samples 174 Are the test procedures valid? 176 Hypothesis tests and confidence intervals 176 Independent and dependent samples 177 Discussion of hypothesis testing 180 Summary 182 Key terms and concepts 182 Problems 183 Reference 186 Answers to exercises 187 SFE_A01.qxd 3/23/07 10:06 AM Page viii 6 The χχ 2 and F distributions 190 Learning outcomes 190 Introduction 190 The χ 2 distribution 191 The F distribution 205 Analysis of variance 207 Summary 214 Key terms and concepts 214 Problems 214 Answers to exercises 217 Appendix: Use of χχ 2 and F distribution tables 219 7 Correlation and regression 220 Learning outcomes 220 Introduction 221 What determines the birth rate in developing countries? 221 Correlation 223 Regression analysis 232 Inference in the regression model 238 Summary 251 Key terms and concepts 252 Problems 252 References 255 Answers to exercises 255 8 Multiple regression 258 Learning outcomes 258 Introduction 259 Principles of multiple regression 260 What determines imports into the UK? 261 Finding the right model 278 Summary 285 Key terms and concepts 286 Problems 286 References 289 Answers to exercises 290 9 Data collection and sampling methods 295 Learning outcomes 295 Introduction 296 Using secondary data sources 296 Using electronic sources of data 298 Collecting primary data 300 The meaning of random sampling 301 Contents ix SFE_A01.qxd 3/23/07 10:06 AM Page ix [...]... school pupils and students are above average in ability and achievement Two types of statistics Figure I.1 Alcohol consumption in the UK The subject of statistics can usefully be divided into two parts, descriptive statistics (covered in Chapters 1 and 10 of this book) and inferential statistics (Chapters 4–8), which are based upon the theory of probability (Chapters 2 and 3) Descriptive statistics are... dispersion The variance The standard deviation The variance and standard deviation of a sample Alternative formulae for calculating the variance and standard deviation The coefficient of variation The standard deviation of the logarithm Measuring deviations from the mean: z scores Chebyshev’s inequality Measuring skewness Comparison of the 2001 and 1979 distributions of wealth The box and whiskers diagram Time-series... variance is a formula for the deviations, which are squared and added up The differences are from the mean, and divided by n or sometimes by n − 1 The bad explanation is a failed attempt to explain the formula for the variance and gives no insight into what it really is The good explanation tries to convey the meaning of the variance without worrying about the formula (which is best written down) For a (statistically)... xvi SFE_A02.qxd 3/23/07 11:55 AM Page 1 Introduction Statistics is a subject which can be (and is) applied to every aspect of our lives A glance at the annual Guide to Official Statistics published by the UK Office for National Statistics, for example, gives some idea of the range of material available Under the letter ‘S’, for example, one finds entries for such disparate subjects as salaries, schools,... the book It is helpful if students are comfortable manipulating equations so if some revision is required I recommend one of the following books: I Jacques, Mathematics for Economics and Business, Prentice Hall, 2003 E.T Dowling, Mathematics for Economists, Schaum’s Outline Series in Economics, McGraw-Hill, 1986 J Black and J Bradley, Essential Mathematics for Economists, 2nd edn, Wiley, 1980 Author... methods is therefore to summarise all this information and draw out the main features, without distorting the picture Consider, for example, the problem of presenting information about the wealth of British citizens (which follows later in this chapter) There are about 17 million households on which data are available and to present the data in raw form (i.e the wealth holdings of each and every family)... numbers) and 7 (Data collection and sampling methods) have been moved to the end of the book This allows a continuous development from descriptive statistics, through probability concepts, to statistical inference in the first part of the book This will suit many courses which concentrate on the use of statistics and which do not wish to focus on data collection Index numbers and data collection now form... data on birth rate, GNP, growth and inequality and table p45 Data to analyse birthrate from Economic Development for a Developing World, 3rd ed, Pearson Education (Todaro, M); ‘Cohabitation: not for long but here to stay’ from Journal of Royal Statistical Society, Series A, 163 (2), Blackwell Publishing (Ermisch J and Francesconi M, 2000); Tab 10.26 from Real GDP per capita for more than one hundred countries... Publishing (Kravis, Heston and Summers 1978); Table p197 ‘Road accidents and darkness from some effects on accidents of changes in light conditions at the beginning and end of British Summer Time’, Supplementary Report 587, Transport and Road Research Laboratory (Green H, 1980) In some instances we have been unable to trace the owners of copyright material, and we would appreciate any information that would... answers and commentary on exercises n Downloadable PowerPoint slides n For more information please contact your local Pearson Education sales representative or visit www.pearsoned.co.uk/barrow SFE_A01.qxd 3/23/07 10:06 AM Page xii SFE_A01.qxd 3/23/07 10:06 AM Page xiii Preface to the fourth edition This text is aimed at students of economics and the closely related disciplines of accountancy and business, . Images 027368308X_COVER 3/23/07 12:29 PM Page 1 Statistics for Economics, Accounting and Business Studies Visit the Statistics for Economics, Accounting and Business Studies, fourth edition Companion Website. 0-273-68308-X www.pearson-books.com An imprint of Statistics for Economics, Accounting and Business Studies Barrow fourth edition New to this edition: More worked examples and real life business applications show. bodies. Statistics for Economics, Accounting and Business Studies fourth edition Michael Barrow ‘An excellent reference book for the undergraduate student; filled with examples and applications