Statistics for economics accounting and business studies 7th edtion micheal barrow

Seventh Edition STATISTICS FOR ECONOMICS, Accounting and Business Studies MICHAEL BARROW Statistics for Economics, Accounting and Business Studies At Pearson, we have a simple mission: to help people make more of their lives through learning We combine innovative learning technology with trusted content and educational expertise to provide engaging and effective learning experiences that serve people wherever and whenever they are learning From classroom to boardroom, our curriculum materials, digital learning tools and testing programmes help to educate millions of people worldwide – more than any other private enterprise Every day our work helps learning flourish, and wherever learning flourishes, so people To learn more, please visit us at www.pearson.com/uk Statistics for Economics, Accounting and Business Studies Seventh edition Michael Barrow Harlow, England • London • New York • Boston • San Francisco • Toronto • Sydney • Dubai • Singapore • Hong Kong Tokyo • Seoul • Taipei • New Delhi • Cape Town • São Paulo • Mexico City • Madrid • Amsterdam • Munich • Paris • Milan Pearson Education Limited Edinburgh Gate Harlow CM20 2JE United Kingdom Tel: +44 (0)1279 623623 Web: www.pearson.com/uk First published 1988 (print) Second edition published 1996 (print) Third edition published 2001 (print and electronic) Fourth edition published 2006 (print and electronic) Fifth edition published 2009 (print and electronic) Sixth edition published 2013 (print and electronic) Seventh edition published 2017 (print and electronic) © Pearson Education Limited 1988, 1996 (print) © Pearson Education Limited 2001, 2006, 2009, 2013, 2017 (print and electronic) 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 The print publication is protected by copyright Prior to any prohibited reproduction, storage in a retrieval system, distribution or transmission in any form or by any means, electronic, mechanical, recording or otherwise, permission should be obtained from the publisher or, where applicable, a licence permitting restricted copying in the United Kingdom should be obtained from the Copyright Licensing Agency Ltd, Barnard’s Inn, 86 Fetter Lane, London EC4A 1EN The ePublication is protected by copyright and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased, or as strictly permitted by applicable copyright law Any unauthorised distribution or use of this text may be a direct infringement of the author’s and the publisher’s rights and those responsible may be liable in law accordingly Contains public sector information licensed under the Open Government Licence (OGL) v3.0 http://www nationalarchives.gov.uk/doc/open-government-licence/version/3/ Pearson Education is not responsible for the content of third-party internet sites ISBN: 978-1-292-11870-3 (Print) 978-1-292-11874-1 (PDF) 978-1-292-18249-0 (ePub) British Library Cataloguing-in-Publication Data A catalogue record for the print edition is available from the British Library Library of Congress Cataloging-in-Publication Data Names: Barrow, Michael, author Title: Statistics for economics, accounting and business studies / Michael  Barrow Description: Seventh edition | Harlow, United Kingdom : Pearson Education,   [2017] | Includes bibliographical references and index Identifiers: LCCN 2016049343 | ISBN 9781292118703 (Print) | ISBN 9781292118741   (PDF) | ISBN 9781292182490 (ePub) Subjects: LCSH: Economics Statistical methods | Commercial statistics Classification: LCC HB137 B37 2016 | DDC 519.5024/33 dc23 LC record available at https://lccn.loc.gov/2016049343 10 21 20 19 18 17 Print edition typeset in 9/12pt StoneSerifITCPro-Medium by iEnergizer Aptara® Ltd Printed in Slovakia by Neografia NOTE THAT ANY PAGE CROSS REFERENCES REFER TO THE PRINT EDITION For Patricia, Caroline and Nicolas This page intentionally left blank Contents Guided tour of the book Publisher’s acknowledgements Preface to the seventh edition Custom publishing Introduction Descriptive statistics Learning outcomes Introduction Summarising data using graphical techniques Looking at cross-section data: wealth in the United Kingdom in 2005 Summarising data using numerical techniques The box and whiskers diagram Time-series data: investment expenditures 1977–2009 Graphing bivariate data: the scatter diagram Data transformations The information and data explosion Writing statistical reports Guidance to the student: how to measure your progress Summary Key terms and concepts Reference Formulae used in this chapter Problems Answers to exercises Appendix 1A: Σ notation Problems on Σ notation Appendix 1B: E and V operators Appendix 1C: Using logarithms Problems on logarithms 2 Probability Learning outcomes Probability theory and statistical inference The definition of probability Probability theory: the building blocks Events Bayes’ theorem Decision analysis xii xiv xvi xviii 8 10 16 27 47 48 63 67 70 72 74 75 75 76 77 78 84 88 89 90 91 92 93 93 94 94 97 98 110 112 vii Contents Summary Key terms and concepts Formulae used in this chapter Problems Answers to exercises Probability distributions Learning outcomes Introduction Random variables and probability distributions The Binomial distribution The Normal distribution The distribution of the sample mean The relationship between the Binomial and Normal distributions The Poisson distribution Summary Key terms and concepts Formulae used in this chapter Problems Answers to exercises Estimation and confidence intervals Learning outcomes Introduction Point and interval estimation Rules and criteria for finding estimates Estimation with large samples Precisely what is a confidence interval? Estimation with small samples: the t distribution Summary Key terms and concepts Formulae used in this chapter Problems Answers to exercises Appendix: Derivations of sampling distributions Hypothesis testing Learning outcomes Introduction The concepts of hypothesis testing The Prob-value approach Significance, effect size and power Further hypothesis tests Hypothesis tests with small samples Are the test procedures valid? Hypothesis tests and confidence intervals viii 116 117 118 118 124 128 128 129 130 131 137 145 151 153 156 156 157 157 162 164 164 165 165 166 170 173 181 186 187 188 188 191 193 195 195 196 196 203 204 207 211 213 214 Contents Independent and dependent samples Issues with hypothesis testing Summary Key terms and concepts Reference Formulae used in this chapter Problems Answers to exercises 6 The X2 and F distributions Learning outcomes Introduction The x2 distribution The F distribution Analysis of variance Summary Key terms and concepts Formulae used in this chapter Problems Answers to exercises Appendix Use of x2 and F distribution tables Correlation and regression Learning outcomes Introduction What determines the birth rate in developing countries? Correlation Regression analysis Inference in the regression model Route map of calculations Some other issues in regression Gapminder again Summary Key terms and concepts References Formulae used in this chapter Problems Answers to exercises Multiple regression Learning outcomes Introduction Principles of multiple regression What determines imports into the United Kingdom? Finding the right model 215 218 219 220 220 221 221 226 230 230 231 231 245 248 255 255 256 256 259 261 263 263 264 265 267 276 283 291 293 297 298 299 299 300 301 304 307 307 308 309 310 330 ix www.downloadslide.com Index median 32–3, 34, 442 Microsoft Excel see Excel mid-point 28 minimax regret criterion 114–15 modal class interval 20 mode 34–5 model selection 330–8 moving averages 424–6 multi-stage sampling 358, 363, 370 multi-tasking 210–11 multicollinearity 337 multiple bar chart 11–12 multiple regression 307–48 determinants of imports into United Kingdom 308, 310–30 finding right model 330–8 principles of 309–10 multiple time-series graph 53–6 multiplication by constant 69 using logarithms 91 multiplication rule 102 combining addition rule and 106–7 multiplicative model 423 mutually exclusive 97 mutually exclusive events 100 natural logarithms 92 negative autocorrelation 329 negative correlation 267, 268 net present value (NPV) 395, 444, 447 95% confidence interval 171–81, 444 nominal scale non-linear 49 non-linear transformation 294–6, 325 non-parametric statistics 272 non-rejection region 198 Normal distribution 129–30, 137–45, 444 and Binomial distribution, relationship between 151–2 parameters 138–9 of sample mean 145–51 standard 140, 451 null hypothesis 196, 200, 202, 204 numerical techniques 2, 27–47 measure of dispersion 27, 35–45 measure of location 27–35 measure of skewness 27, 45–6 496 Office of National Statistics (ONS) 48, 353, 354 oil reserves 148–9 omitted variable bias (OVB) 331, 334–5 one-tail test 199–201, 204, 262 one-way analysis of variance 248 online data 353 sources of 70–2, 297–8, 350 operators 100 E 30, 90, 141 V 90, 141 ordinal scale ordinary least squares (OLS) 279, 283 outcomes, of experiment 97 outliers 47, 51 Paasche price index 382–3, 443, 447 Laspeyres index vs 383, 386–7 Paasche quantity index 388–9, 443, 447 paired samples 215, 216–18 parameters, of distribution 130 Binomial distribution 132–4 Normal distribution 138–9 Pearson’s product-moment correlation coefficient 273 Penn World Tables 354 percentage 13, 49 percentiles 33 perfect information defined 115 expected value of 116 permutations 108–9 pie charts 15–16 point estimate 165–6 Poisson distribution 153–5 pooled variance 185 population mean 30, 442 population variance 39, 40, 442 positive autocorrelation 328 positive correlation 267 positively skewed 45 posterior beliefs 96 posterior probabilities 111 power, of test 205 powers 91–2 precision 166, 167–8 bias and, trade-off between 169–70 prediction 289–93 prediction interval 290 present value 113, 395, 444, 447 www.downloadslide.com Index presentation tables 73 price index 46, 377–85 CPI 351–2, 375, 393–4 current-year weights 378–81 expenditure weights 385–7 Laspeyres index see Laspeyres price index Paasche index 382–3, 386–7, 443, 447 quantity index/expenditure index and 389–91 RPI 351–2, 375 units of measurement 383–5 primary data 350, 355 prior beliefs 96 prior information 201 prior probability 111 Prob-value 203–4, 288 probability distributions 128–63 Binomial distribution 129–30, 131–7, 151–2 defined 129 Normal distribution 129–30, 137–45, 151–2 Poisson distribution 153–5 random variables 129, 130–1 sample mean distribution 145–51 probability interval 150–1 probability/probability theory 93–127 Bayes’ theorem 110–12 building blocks 97–8 conditional 104, 106–7 decision analysis 112–16 defined 94–6 frequentist view 95–6 joint 107 marginal 107 of outcome 97–8 posterior 111 prior 111 statistical inference 94 subjective view 96 proportion 13–14, 49, 95 estimating 175–6, 180–1, 186, 209–10 testing 207–8 quantiles 33 quantity index 387–9 price index/expenditure indiex and 389–91 quantity series 390 quartiles 33 quintiles 33 quota sampling 358, 364–5 R2 see coefficient of determination railway accidents 155 random component 423 random elements 422 random number tables 368, 449–50 random residual 434 random sampling 356–65 cluster sampling 358, 362 multi-stage sampling 358, 363, 370 quota sampling 358, 364–5 simple 357, 358 stratified sampling 357, 358–61, 370 random variables 129, 130–1 range 36–7 rank correlation coefficient 272–6 ratio scale 9, 16 real interest rate 390, 397–8 real terms 390 transforming to 313 reciprocal transformation 69, 296 record of data sources 353 reference tables 73 reference year 376 regression analysis 264, 276–82 analysis of errors 283–5 confidence interval estimates 285–6, 446 F test 287–8 hypothesis testing for coefficients 286–7 inference in regression model 283–93 interpreting computer output 288–9 measurement problems 294 multiple see multiple regression non-linear transformations 294–6 prediction 289–93 units of measurement 293–4 regression line 277–82 calculation 278–9 interpretation of slope and intercept 279–80 measuring goodness of fit 280–2 regression plane 309–10 regression sum of squares (RSS) 281, 446 rejection region 198, 232, 234 relative dispersion 42 relative frequency distribution 21–6 residual see error term/residual response variable 248 retail price index (RPI) 351–2, 375 road accidents 237–40 497 www.downloadslide.com Index roots 91–2 rounding 68 sample mean 30, 442 estimating difference between 177–80, 184–5, 208–9, 212–13 estimation for large sample 170–3 estimation for small sample 183–5 hypothesis testing 196–203, 211–13 sampling distribution of 145–51 sample space 97, 101 sample variance 39, 40, 442 sampling 356–70 collecting sample 367–70 methods 358–65 from non-Normal population 149–51 random 356–65 sample size calculation 365–7 sampling distributions 145–51, 176, 178 derivation of 193–4 sampling errors 371 sampling frame 367, 368, 370–1 scatter diagrams 2–3, 63–5, 314–15 seasonal adjustment, time-series data 421–35 components of time series 421–32 forecasting 432–3 using adjusted or unadjusted data 434 seasonal component 423 seasonal dummy variables 335–7 seasonal factors 424 seasonally adjust 424 secondary data sources 350, 351–5 checking data 354–5 collecting right data 351–2 up-to-date figures 352 semi-log transformation 296 serial correlation 50 sigma (π) notation 88–90 significance level 198 choice of 202–3 simple random sampling 357, 358 simultaneous equation model 310 skewness 20 coefficient of 45–6, 443 defined 45 measures of 27, 45–6 slope of regression line 446 interpretation of 279–80 small samples 498 estimation 181–6 hypothesis testing with 211–13 smoothing data 424 moving average 424–6 Spearman’s coefficient of rank correlation 273, 445, 462 specific to general approach 331 spreadsheet packages 308 see also Excel spurious regression 330 stacked bar chart 12 standard deviation 38–9 alternative formulae for calculating 40–1 of logarithm 43–4 sample 39 standard errors 147, 285, 289 standard Normal distribution 140, 451 standard width 17 states of the world 112 statistical inference see inference statistical reports 72–5 graphs in 74 tables in 73–4 writing 73 statistical significance 204–5 strata 359 stratification factor 360 stratified sampling 357, 358–61, 370 student distribution see t distribution subjective view 96 sums of squares 250–2 surveys Family Resources Survey 399 interviewing techniques 355–6 Living Costs and Food Survey 370–1 telephone 369 UK Time Use Survey 363–4 systematic components 422 t distribution 285 estimation with small samples 181–6 percentage points of 452 test for paired examples 216–18 testing difference of two means 212–13 teenage weapons 134–5 telephone surveys 369 test statistic 445, 448 calculation of 243–5 correlation 269 www.downloadslide.com Index difference of two means 209 proportion testing 207–8 sample mean 199, 212 testing hypotheses 165 time preference 394 time series, components of 421–32 time-series data 9–10, 48–63, 308–9 geometric mean 60 mean 58–9 seasonal adjustment of see seasonal adjustment, time-series data variance 62–3 time-series graph 49, 50 multiple 53–6 time trends 336 Todaro, M 265–6 total sum of squares (TSS) 281, 446 ANOVA 250, 445 tree diagrams 103 trend 49, 336, 423 isolating 424–6 trial 97 two-tail tests 199–201, 204, 261 Type I and Type II errors 197, 198, 202–3 UK Living Costs and Food Survey 370–1 UK Time Use Survey 363–4 unbiased estimate, of population variance 39 unbiased estimator 166 unemployment forecasting 432–3 seasonal adjustment of time-series data 421–32 uniform distribution 234 union, of sets 101 units of measurement independence of 42 price index 383–5 regression coefficients 293–4 V operator 90, 141 validity of test procedures 213 value index see expenditure index variance 4, 37–8, 90 alternative formulae for calculating 40–1 of Binomial distribution 135–7 error 250 of error term 446 estimation with x2 distribution 232–4 of intercept 446 pooled 185 population 39, 40, 442 sample 39, 40, 442 of slope coefficient 446 testing equality of two 245–7 of time series 62–3 variance ratio test 246 Venn diagram 101, 102 volume series 390 volume terms 390 wage-price spiral 272 wealth distribution 9, 16–64 comparison of 2005 and 1979 distributions 46–7 frequency tables and charts 16–18 histograms 18–21 measure of dispersion 27 measure of location 27–35 measure of skewness 27, 45–6 relative and cumulative frequency distributions 21–6 weighted average 30–1, 365 Wilcoxon’s Sign Test 229 within sum of squares 250, 251–2, 445 World Bank 319, 354 World Economic Database 354 XY charts (scatter diagrams) 2–3, 63–5, 314–15 Yahoo Finance 72 z score 44, 140–1, 443, 444 zero correlation 267 499 ... learn more, please visit us at www.pearson.com/uk Statistics for Economics, Accounting and Business Studies Seventh edition Michael Barrow Harlow, England • London • New York • Boston • San Francisco... If you are teaching an introductory statistics course for economics and business students, you also teach an introductory mathematics course for economics and business students? If you do, you... for the print edition is available from the British Library Library of Congress Cataloging-in-Publication Data Names: Barrow, Michael, author Title: Statistics for economics, accounting and business