Quantitative Methods for Business Decisions

Fifth edition

Jon Cunvin and Roger Slater

MCAST 0 THOMSON

Australia - Canada . Mexico . Singapore . Spain . United Klngdom United States

Contents

Preface xiv

Part 1 Quantitative information 1

Introduction 1 The questionnaire 3 The coding sheet 4 Visit the website 5 Quick start: Quantitative in formation 6

Chapter 1 The quantitative approach 7

Objectives 7 1.1 Problem solving 8 1.2 Methodology 12 1.3 Models 15 1.4 Measurement 22 1.5 Scoring models 24 1.6 Conclusions 27 1.7 Problems 2 8

Chapter 2 Managing data 31

Chapter 3

Objectives 2.1 Issues of data collection 2.2 Published sources 2.3 Internet sources 2.4 A census or a sample? 2.5 Market research 2.6 Conclusions 2.7 Problems

Survey methods

Objectives 3.1 Probability sampling 3.2 Non-probability sampling

Contents

3.3 Survey design 3.4 Questionnaire design 3.5 Non-response 3.6 Conclusions 3.7 Problems

Cha~ter 4 Presentation of data

Objectives 4.1 Raw data 4.2 Tabulation of data 4.3 Visual presentation 4.4 Presentation of continuous data 4.5 Graphical representation 4.6 Conclusions 4.7 Problems Part l Conclusions

!part 2 Descriptive statistics 99

Introduction 9 9 Quick start: Descriptive statistics - 101

Chapter 5 Measures of location 103

Chapter 6

Objectives 5.1 The mean, median and mode 5.2 Other measures of location 5.3 Conclusions 5.4 Problems

Measures of dispersion

Objectives 6.1 The standard deviation 6.2 Other measures of dispersion 6.3 Relative measures of dispersion 6.4 Variability in sample data 6.5 Conclusions 6.6 Problems 6.7 Appendix

r

Contents vii l

Chapter 7 Index numbers 145

Objectives 7.1 The interpretation of an index number 7.2 The construction of index numbers 7.3 The weighting of index numbers 7.4 The Retail Prices Index 7.5 Conclusions 7.6 Problems Part 2 Conclusions

Part 3 Measuring uncertainty 167

Introduction Organization of Part 3 Quick start: Measuring uncertainty

Cha~ter 8 Probability 1 7 1

Objectives 8.1 Basic concepts 8.2 Definitions 8.3 Basic relationships in probability 8.4 Probability trees 8.5 Expected values 8.6 Decision trees 8.7 Bayes' theorem 8.8 Markov chains 8.9 Conclusions 8.10 Problems

Chapter 9 Discrete probability distributions

Objectives 9.1 Uniform distribution 9.2 Binomial distribution 9.3 Poisson distribution 9.4 Poisson approximation to the binomial 9.5 Conclusions 9.6 Problems

1 viii Contents

Chapter l 0 The Normal distribution 220

Objectives 10.1 Characteristics of the Normal distribution 10.2 The standard Normal distribution 10.3. Combinations of variables 10.4 Central limit theorem 10.5 Normal approximations 10.6 Conclusions 10.7 Problems Part 3 Conclusions

Part 4 Statistical inference 239

Introduction 23 9 Quick start: Inference quick start 243

Chapter 11 Confidence intervals 245

Objectives 1 1.1 Statistical inference 1 1.2 Inference about a population 1 1.3 Confidence interval for the population mean 1 1.4 Confidence interval for a population percentage 1 1.5 The difference between independent samples 1 1.6 The finite population correction factor 1 1.7 The t-distribution 11.8 Confidence interval for the median - large sample

approximation 1 1.9 Conclusions 1 1.10 Problems

Chapter 12 Significance testing 275

Objectives 12.1 Significance testing using confidence intervals 12.2 Hypothesis testing for single samples 12.3 One-sided significance tests 12.4 Types of error 12.5 Hypothesis testing with two samples 12.6 Hypothesis testing with small samples 12.7 Conclusions 12.8 Problems

Contents ix 1

Chapter 13 Non-parametric tests 3 0 1

Objectives 13.1 Chi-squared tests 13.2 Mann-mitney U test 13.3 Wilcoxon test 13.4 Runs test 13.5 Conclusions 13.6 Problems Part 4 Conclusions

Part 5 Relating variables and predicting outcomes 331

Quick start: Relating variables and predicting outcomes 333

Chapter 1 4 Time series 335

Objectives 14.1 Time series models 14.2 The trend 14.3 The seasonal factors 14.4 The cyclical factors 14.5 The residual or random factor 14.6 Predictions 14.7 Exponentially weighted moving averages 14.8 Summary and conclusions 14.9 Problems

Chapter 15 Correlation

Objectives 1 5.1 Scatter diagrams 15.2 Cause and effect relationships 15.3 Measuring linear association 15.4 The coefficient of determination 15.5 Measuring non-linear association 15.6 Testing the significance of the correlation 15.7 Conclusions 15.8 Problems 15.9 Derivation of the correlation coefficient 15.10 Algebraic link between Spearman's and Pearson's

coefficients

I X Contents

Chapter 16 Regression 390

Objectives 16.1 Linear regression 16.2 The graph of the regression line 16.3 Predictions from the regression line 16.4 Another regression line 16.5 Interpretation 16.6 Non-linear relationships 16.7 Conclusions 16.8 Problems 16.9 Appendix

Chapter 17 Multiple regression and correlation 409

Objectives 1 7.1 The basic two-variable model 17.2 The effects of adding variables 17.3 Assumptions and econometric problems 17.4 Analysis of a multiple regression model 17.5 Using multiple regression models 1 7.6 Conclusions 17.7 Problems Part 5 Conclusions

Part 6 Modelling 435l

Introduction 435

Chapter 18 The time value of money 437

Objectives 18.1 Interest: simple and compound 18.2 Depreciation 18.3 Present value 18.4 The internal rate of return 18.5 Incremental payments 18.6 Annual percentage rate (APR) 18.7 Conclusions 18.8 Problems 18.9 Appendix

1

Contents xi I

Chapter 19 Linear programming 457

Objectives 19.1 Definition of a feasible area 19.2 The solution of a linear programming problem 19.3 Special cases 19.4 The value of resources 19.5 Computer-based solutions 19.6 Conclusions 19.7 Problems

Chapter 20 Networks 483

Objectives 20.1 Notation and construction 20.2 The critical path 20.3 Measures of float 20.4 Gantt charts and managing resources 20.5 Project time reduction 20.6 Uncertainty 20.7 Computer-based solutions to network problems 20.8 Conclusions 20.9 Problems

Chapter 2 1 Modelling stock control and queues 514

Chapter 22

Objectives 2 1.1 Introduction to the economic order quantity model 2 1.2 Quantity discounts 2 1.3 Non-zero lead time 2 1.4 Introduction to modelling queues 2 1.5 A model for a single queue 2 1.6 Queues - modelling cost 2 1.7 Modelling multi-channel queues 2 1.8 Conclusions 2 1.9 Problems 2 1.10 Appendix - proof of EBQ

Simulation

Objectives 22.1 An introduction to simulation models 22.2 Developing a simple simulation model 22.3 Random event generation

/ xii Contents 1 22.4 The construction of a simulation model 540 22.5 Building a simulation model using a spreadsheet 542 22.6 Conclusions 544 22.7 Problems 544 I

Part 6 Conclusions 546 '

Part 7 Mathematical background 547

Introduction 547

Chapter 23 Mathematical relationships 549

Objectives 23.1 Introduction to algebra 23.2 Powers 23.3 Arithmetic and geometric progressions 23.4 Functions 23.5 Conclusions 23.6 Problems 23.7 Proof of AP 23.8 Proof of GP 23.9 Proof of quadratic formula

Chapter 24 Matrices 576

Objectives 24.1 What is a matrix? 24.2 Matrix manipulation 24.3 Solutions of simultaneous equations 24.4 Leontief input-output analysis 24.5 Conclusions 24.6 Problems

Chapter 25 Use of calculus

Objectives 25.1 Differentiation 25.2 Economic applications I 25.3 Turning points 25.4 Economic applications I1 25.5 Further notes 25.6 Integration

7 contents xiii I

25.7 Economic summary 616 25.8 Functions of more than one variable 61 7 25.9 Maximization and minimization subject to constraints 620 25.10 Conclusions 623 25.1 1 Problems 623 Part 7 Conclusions 628

Appendices 629

Cumulative binomial probabilities 63 1 Cumulative Poisson probabilities 632 Areas in the right-hand tail of the Normal distribution 633 Student's t critical points 63 5

critical values 63 6 Present value factors 63 8 Mann-Whitney test statistic 640 Wilcoxon test statistic 643 Runs test 644 Durbin-Watson statistic 646 Random number table 648

Answers 649

Index

Index

Absorbant state 191 Accuracy 40 Activities 483, 484 Activity on arrow 484, 485 Activity on node 484 Adding variables 226 Adding variances 26 1 Addition of matrices 578 Additive model 338, 249, 338,

349,355, 357 Additive scoring model 25 Adjunct matrix 584 Adjusted R' 412 Admap 36 Aggregate index 152 Algebra 550ff. Alternative hypothesis 278, 279,

283, 286, 304, 316, 319, 322

Analogue model 17, 433 Analysis 2, 16, 99 Analytical model 20, 21 Annual Abstract of Statistics 36 Annual percentage rate (APR)

45 1 Annuities 450 Arithmetic mean 104 Arithmetic progression 554, 574 Array 557 C

Association 303, 371 Assumption 6, 18 Attitude scale 71 Autocorrelation 41 8ff., 421,

424 Automatic interaction detection

technique 137 Average 20, 174, 183, 350 Average arrival rate 524 Average cost 604 Average price relative index 153 Average revenue 604, 605, 616 Average service rate 524 Average stock level 515 Axiomatic definition, probability

177, 178

Bar charts 22, 76ff:, 81, 204, 205, 213

Baseyear 146 147 154 Base-weighted index 1 54 Basket of goods 147, 153, 156,

159 Bayes' theorem 188ff. Best fit 392 Beta distribution 496 Bias 6, 31, 32, 38, 39, 44, 49, 52,

54, 58, 61, 245 Binomial distribution 169, 206ff.,

236,231, 269, 311, 538 Brainstorm 11 Break-even 16, 2 1, 225, 550 Business significance 13 8, 15 1,

247,281

Calculus 596ff. Capital recovery factor 45 1 Cardinal data 104, 371, 373, 376,

390 Categorical data 22.23, 104, 297 Cause and effect 35, 367, 368ff.,

380 Census 6, 34, 36, 38, 39, 239,

245, 247, 263 Census of Population 50 Central Limit Theorem 227ff.,

243, 246, 251, 252, 257, 2 63

Central Statistical Office (CSO) 35 Centred trend 346 Centred four-point moving

average trend 346 Chance 167, 171 Chi-squared 174, 243, 302ff. Checklists 53 Classical definition, probability

1 75 Clustering algorithms 136ff. Clusters 48 Cobb-Douglas production

function 622 Coding 58, 60 Coefficient 560 Coefficient of correlation 371

Coefficient of determination 376, 412,413

Coefficient of skewness 135 Coefficient of variation 135 Cofactors 583 Column vector 577 Combinations 2 10 Combinations of variables 226ff. Common difference 554 Common ratio 556 Commutative 579 Complexity 16 Component bar chart 76ff. Compound interest 439ff. .

Computers 20 Computational model 20 Conditional probability 180 Confidence interval 243, 245ff.,

251, 254, 257, 261, 262, 266, 275, 277, 394, 396, 413, 497

Confidence interval for a percentage 257

Confidence interval for the mean 250ff.

Confidence interval for the median 269

Confidence interval for difference of means 26 1

Confidence interval for difference of percentages 262

Confidence level 247, 381 Confidence limits 4 13 Conformable for addition 578 Conformable for multiplication

580 Constant function 558 Constraint 458, 460 Consumers risk 287 Continuous data 24, 74, 83ff.,

104, 110, 127 Continuous distribution 220 Continuous probability

distributions Contribution to profit 552 Controllable variable 390, 534 Convenience sampling 52

Index

483, 487ff., 494,

Critical value 279, 284 Cross tabulation 51, 74, 173, 303 Cubic function 570 Current-weighted index 154 Cyclical factor 338, 35 1, 353ff.

Data 1, 6, 22, 31, 32, 34, 38, 44, 67ff.

Database 38 Data collection 34 Datastream 37 Decision making 25, 27, 186 Decision trees 185ff. Deductive 14 Definite integration 6 15 Degrees of freedom 265, 304 Delivery and collection 56 Delphi technique 177 Demand function 562, 604 Dependent events 1 82 Dependent variable 88 Depreciation 44 lff. Derivative 600 Descriptive statistics 15, 99,

103ff. Deseasonalized data 357 Desk research 1, 13, 35 Determinant of a matrix 583 Deterministic model 17, 19 Deterministic relationship 1 67,

171,367 Detrended data 357 Diagrams 67ff. Diaries 56 Dichotomous variable 206 Difference between independent

samples 260 Difference of means 291ff. Difference of percentages 292 Differentiation 597ff. Directed graph 190 Discounting 443 Discounts 51 9 Discount rate 444 Discrete data 24, 72, 74, 76ff.,

104, 108, 126, 127 Discrete distribution 294ff.

Discrete probability distributions 203ff.

Dispersion 123ff. Distribution of sample means 25 1 Disturbance term 4 16, 41 8 Domain 558 Doughnut 82 Dummy activity 484, 486 Dummy variable 34 1 Duration of project 488 Durbin-Watson test 4 18

Earliest starting time (EST) 487, 488

Econometrics 41 6 Economic batch quantity (EBQ)

515 Economic order quantity (FOQ)

5 15ff. Economic Trends 36 Elasticity of demand 605 Electoral Register 46, 47, 49 Elements of a matrix 577 E-mail 56 Endogenous variable 400 Equality of matrices 578 Equally likely 19, 175 Equations 390, 557ff. Equilibrium 562 Error, type of 287 Estimate 1 10 Estimator 254 Euler's constant 570 European Official Statistics: a

guide to databases 36 European Official Statistics:

sources of information 36 Europe in Figures 36 Eurostat Handbook 36 Event 484ff. EXCEL 42, 69, 70, 72, 74, 106,

1 14, 133,409,470 Exogenous variable 400, 534 Experimentation 533 Expectations 183ff., 213 Expected cell frequencies 305 Expected frequencies 305, 307 Expected monetary value 183,

187 Expected number 213 Expected outcome 174 Expected value 19, 174, 183,

305, 536

Expert systems 20, 21 Explanatory variables 41 7 Exponential function 570, 600,

612 Exponentially weighted moving

average 357ff. Extrapolation 397

Face to face interviews 40 Factorial 2 10 Family Expenditure Survey 16, 56,

159 Feasible area 458, 459, 461, 465 Feasible space 458 Filter questions 59, 62 Financial statistics 36 Finite population correction factor

263, 264 First order conditions 407 Five-bar gate 70 Fixed cost 61 5 Formulation 457, 541 Free float 490, 494 Frequency 69, 70, 72, 84, 108,

126 Frequency definition of probability

176, 536 Function 557ff., 61 7 Function of a function rule 6 12

Gallup 40, 58, 60 Gantt charts 491ff., 501ff., 504 Gantt chart screen 498 General Index of Retail Prices

( P I ) 145, 158ff. Geometric mean 1 15, 1 16 Geometric progression 554, 556,

5 75 Goodness of fit 309 Government statistical service 36 Government statistics 36 Gradient 597, 603 Graphs 85ff. Group discussions 34.40 Guide to Official Statistics 35

Harmonic mean 1 15, 1 16 Heteroskedasticity 420 Histograms 83ff., 113, 23 1 Holding costs 5 15 Horizons 36 Hypotheses 275, 277

m . Index 679 1 Hypothesis testing 278ff., 412, Least squares line 392 Median 101, 104, 105, 108, 111,

419 Leontief input-output analysis 112, 130,269 589 Methodology 12ff., 27, 39, 44ff.

Level of accuracy 40 Microsoft Project for Windows Iconic model 17, 433 Level of confidence 256 497ff. Idea generation 10 I

Identity matrix 58 1, 583 Level of measurement 22 Mid-point 1 10, 127 i *

Imaginary roots 568 Line of best fit 392 Minimization 464 !

Incremental payments 449ff. Line of equality 90 Minimum 606, 618 independent events 169, 179, Linear association 371 MINITAB 74, 99,409

182,305 Linear depreciation 441 MINTEL 36 Independent float 490 Linear function 391, 416, 558, Mode 101, 104, 105, 109, 113

Independent samples 260ff. 560 Model 8, 15, 17, 28 Independent variable 88 Linear programming 457ff., 558, Modelling 8, 15ff., 433ff.

Index linked 158 577 Monthly Digest of Statistics 36 Index numbers 101, 145ff. Linear regression 341, 391 Mortgages 45 1 Inductive 14 Linear relationship 367 Moving average trend 343ff.

Inequality 459 Linear trend 341 Multi-stage sample 48 Literary Digest survey 55 Multichannel queues 528ff. Inference 32, 39, 239, 247

I l

information 6, 22, 3 1 Log graph 88 Multicollinearity 41 7ff., 42 1 I Longitudinal study 57 Multiple R 412 Initial vector 19 1

Input-output analysis 589ff. Look-up tables 535, 540 Multiple regression 409ff., 577 Input-output coefficients 590 Lorenz curve 89, 90, 560 Multiplication of matrices 580 1 Input variables 534 Lower quartile 13 1 Multiplicative model 339, 351, instantaneous change 600 355,357 Integration 6 13ff. Multiplicative ranking model 26

Intercept 560 MALTHUS 41 7 Mutually exclusive 169, 178 Mann-Whitney U test 315ff.

l ll : i Interest 438ff. I

Internal rate of return 445ff. Marginal analysis 470

Internet 1, 6, 20, 31, 35, 37ff., Marginal cost 603, 604, 615 National statistics 35 ~ 5 6 Marginal revenue 603 Negative exponential distribution

Marginal value of resources 468 524, 528 1

Interpolation 397, 447 Market research 26, 40ff., 51, 54, NEILSEN 36, 57 l

Interval estimate 250, 270 Interval scale data 22, 23, 297 171, 246, 248,445 Net present value 444, 445, 446, I

1 Interviewer 53 Market Research Society 40 447

Interviewer bias 55 Marketing in Europe 36 Networks 17, 483ff. I Interviews 40, 53ff. Markov Chains 189ff., 577 Node 484

MARQUIS 55, 62, 74 Nominal data 22, 23 I

Inverse of a matrixC582ff. Investment appraisal 171, 443ff. Matched pairs 2957 318 Nominal rate of interest 452

I Mathematical model 17 Nominal values 149

l j Iteration 536

Mathematical relationships 549 Non-independent events 169, 179 1 Matrices 576ff. Non-linear association 377ff.

Joint quota 51 Matrix algebra I 89 Non-linear models 401ff.

I Judgement sampling 52

Maximization 460 Non-linear relationships 377ff., Maximum 606, 618 40 1

Kompass Directory 36 l 1 1

Mean 8, 19, 22, 38, 101, 104, Non-mutually exclusive 169, 178 108, 110, 124, 213, 215, Non-negativity constraints 460,

Lagrangian multipliers 620, 62 1 216, 221, 222, 226, 232, 462,464 Laspeyre index 101, 154, 155 233, 248, 249, 254, 496, Non-parametric tests 30 1 ff.

l 1 1

Latest starting time (LST) 487, 497, 524 Non-participant observation 57 488 Mean of binomial 2 13 Non-probability sampling 49, 52

Law of diminishing returns 367 Measurement 22ff. Non-random sample 49

i i l

Lead time 515, 520, 52 1 Measures of dispersion 123ff. Non-response 46, 56, 63ff. Leading questions 6 1 Measures of location 103ff. Non-zero lead time 520ff. 1 1

; l

F - -P--- -- - -- - - . - - -- .l

1 680 Index I

Normal approximation to Binomial 23 1

Normal approximation to Poisson 233

Normal distribution 9, 124, 169, 220ff., 243, 251, 256, 257, 279, 284, 302, 313, 317, 320, 381, 496, 521, 538, 539

Null hypothesis 277, 283, 288 Numeracy 27

Objective function 460, 461 Observation 34, 55, 57 Observed frequencies 305, 309 Office for national Statistics 35,

162 Office of Population Censuses and

surveys (OPCS) 35 Ogive 1 12 On-line questionnaires 56 One-tailed test 283ff., 286, 380,

412 Open-ended groups 83, 110 Open-ended questions 54, 59, 60 Opportunity cost 468, 473 Optimum point 463 Optimistic time 496 Order of a matrix 577 Order statistics 130 Ordering costs 515 ordinal data 22, 23, 104, 297,

322, 371 Output variable 534

Paasche index 10 1, 154, 155 Panel conditioning 56 Panel mortality 56 Panel survey 56, 261 Parameters 6, 18, 239, 534 Parametric tests 243, 301 Partial differentiation 6 18ff. Participant observation 57 Partitioned matrix 585 Pascal's triangle 2 10, 2 1 1 Payback method 454 Pearson's coefficient of correlation

373,377 Percentage change 146 Percentage depreciation 441 Percentage increase 87 Percentage points 147

Percentages 22, 75ff., 231, 257, 286

Percentiles 124 132 PERT 503 Pessimistic time 496 Phenomenologist 14 Physical model I 7 Pictograms 80 Pie chart 77ff. Pilot stage 52, 58, 61, 260 Piloting the questionnaire 58 Pilot survey 58 Point estimate 250 270 275 Poisson approximation to Binomial

216 Poisson distribution 169, 214ff.,

233, 31 1, 521, 524 528 539 Polynomials 570 Pooled standard deviation 267 Population 33, 39, 44, 245, 247 Population census 39, 50, 63 Population mean 289 Population median 270 Population parameter 239, 248,

275 Population percentage 281, 286 Population proportion 230 Population standard deviation 253,

254,280 Positivist 14 Postmultiply 58 1 Post-stratification 48 Postal questionnaires 55 Postal survey 55 Posterior probability 188 Powers 533 Precedence diagram 503 Precoded questions 55, 59, 60, 71 Predictions 335, 356, 357, 390,

394,400 Predictor variable 88 Premultiply 58 1 Presentation of data 67ff. Present value 440, 442ff. Present value tables 440, 443 Price relative 15 1, 156 Primary data 6, 34, 36, 40, 44ff.,

68 Principal diagonal 581, 583 Prior information 260 Prior probability 188 Probability 171ff., 251, 305, 525 Probabilistic model 17, 19

Probability axioms 177 Probability distributions 204 Probability sampling 45ff., 54 Probability trees 181, 203 Probing 35, 53, 61 Problem definition 10 Problem formulation 10 Problem. solving 7ff., 3 1 Producer's risk 287 Product rule for differentiation

610ff. Profit function 609 Progression 554 Project evaluation and review

technique 483 Project management 483ff. Project time reduction 493ff. Prompt 53, 61 Proportions 230

Quadratic function 446, 564ff., 5 75

Qualitative data 7 Quality control 170, 207 Quantitative data 7 Quantity discounts 5 19ff. Quantity index 155 Quartile deviation 124, 130ff.,

132 Quartile range 132 Quartiles 130 Question coding 60 Question structure 58 Question wording 6 lff. Questionnaire 34 Questionnaire design 58ff. Queue discipline 524, 528 Queues 2 1, 21 6, 514ff., 523ff. Queuing cost 526ff. Quota sample 50ff., 54, 63

R squared 412 Random factor 338. 351, 354ff. Random numbers 45,204, 535,

537 Random sample 45ff., 63, 230,

239, 256 Random walk 48 Range 71, 101, 124ff., 130 Rank 26, 81 Rank correlation 371 ff. Rate of change 596, 598

1 . Index 681 1 Rate of return 444 Scaling 146 Spurious correlation 369 379 Rating scale 22, 60 Scatter diagram 89, 366ff., 391 Standard deviation 8, 22 38 101, Ratio scale data 22, 23 Schematic model 17 124ff., 137, 221, 232, 248, Raw data 68ff. Scoring model 24ff. 249, 265 Real values 149 Reciprocal 379 Recursive relationship 2 14 Regression 333, 34 1, 390ff. Regression line 341, 392 Regression line of X on y 399 Regression line of y on X 392 Relationship 16, 18 Relevant population 33 Reliability 12, 13, 20, 27, 35 Reneging 524 Reorder point 520 Representative 39, 45 Representation 14 Residual factor 338, 354ff. Response (see non-response) 48,

55,56 Response rate 55 Resource levelling 506 Retail business 36 Retail prices 8, 145, 147, 158ff. Risk 170, 287 Risk avoider 186 Risk taker 186 Roots 566ff. Rounding 24, 75,440 Row vector 577 Runs test 321ff.

Sample 34, 38, 39, 227, 239, 247 Sample design 39, 239 Sample mean 248 Sample percentage 257, 258, 262 Sample proportion 230 Sample selection 45, 50 Sample size 40, 229, 239, 247,

256, 259 Sample standard deviation 248,

253, 254 Sample statistic 248 Sample with replacement 47 Sample without replacement 47 Sampling 13, 39, 177, 245 Sampling error 250, 254, 258 Sampling frame 45, 48, 54, 63,

23 0

I Sampling stages 48, 49 Sampling theory 227, 245, 247

i Scalar multiplication 579

scientific method 14 Search engine 13, 38 Seasonal adjustment 8, 348, 351 Seasonal factor 336, 337, 348ff. Secondary data 6, 34, 35, 36, 44,

68 Semi-interquartile range 132 Sequences 554 Sequential sampling procedure

260 Series 554 Service cost 527 Shadow price 468, 470, 473, 476 Sigma 105 Significance 25, 247 Significant difference 275 Significance of correlation 380 Significance level 279, 284, 288 Significance test 243, 275ff. Simple aggregate price index 152 Simple average 103 Simple interest 438 Simple price index 10 1, 15 1 ff. Simple random sampling 45, 46,

245 Simplex method 478 Simulation 20, 21, 206, 524,

533ff. Simultaneous equations 463, 562,

586ff. Single server queue 524 Singular matrix 583 Sinking fund 450 Skew 135 Skewness 135,231 Slack variables 473, 474 Slope 493, 265, 293, 316, 319 Smoothing constant 357, 358 SNAP 42 Snowball sampling 52 Social Trends 36 SOLVER 471ff. Spearman's correlation coefficient

371 Specification 420, 424, 540 Spreadsheet 16 20 67, 70, 72,

77, 82, 99, 101, 114, 157, 343

SPSS 42, 74, 99, 133, 304, 409

Standard Standard

589

error 229, 251, 412 Industrial Classification

Standard Normal distribution 222ff.

Standard Normal variable 222 Statistic 2, 8, 23 Statistical association 304 Statistical inference 239ff. Statistical significance 138, 15 1,

247,380 Statistical theory 15, 124, 129,

32 1 Status variable 534 Stem-and-leaf diagram 84 Stochastic 19, 171 Stochastic events 2 17 Stock control 5 14ff. Straight line graphs 391 Stratification 47ff., 49, 239 Structural constraints 46 1, 464,

466 Subjective 26 Subjective probability 176 Substitution 18 Subtraction of matrices 578 Supply function 561 Survey 6, 22, 39, 53ff., 117, 136,

239 Survey data 254 Survey design 53 Survey methods 44ff. Survey Research Centre 61 Symbolic model 17, 433 Syndicated studies 57 Systematic sampling 48

t-distribution 248, 265ff., 275, 293,380,394,395

t-test 380, 413 Tabulation 69ff., 1 08, 126 Tally count 70 Tangent 60 1 Tasks 483 Technical coefficients 590 Telephone interviews 40, 54 Test of hypothesis 4 12 Test statistic 279 Tests of association 303

Tests of goodness of fit 309 Time estimates 483 Time lags 16, 424 ' Time series 333, 335ff. Time series graph 85ff 335, 337 Total annual cost (TAC) 5 16 Total cost 609, 610, 615 Total float 488, 490 Total revenue 609, 615 Total variable cost (TVC) 5 16 Traffic intensity 525 Transformation 222 Transformation to linearity 378 Transition matrix 190 Transitional probabilities 190 Transpose 584 Trend 336, 337, 340ff. Trial cost 462, 467 Trial profit 462 Turning point 564, 606ff. Type I error 288, 289

Type I1 error 288, 289 Types of data 22ff: Types of error 287ff.

Uncertainty 16, 19, 167ff., 496 Uncontrollable variable 390, 534 Under-identification 4 17, 420 Uniform distribution 169, 204ff.,

309, 540 Upper quartile 13 1 Untabulated data 104, 124 Utilization factor 525

Validity 12, 13, 15, 20, 27 35 Value of money 8 Value index 155 Variable(s) 6, 16, 18 Variability 40 Variability in sample data 136

Index

Variance 125, 129ff., 213, 215, 2 16, 222, 226, 233, 261, 416,496,497

Variance of binomial 2 13 Vector 577

1

Visual presentation 74ff., 366 G 3 :

Web search 9, 37 Website 5, 38, 40 Weighted mean 1 15, 1 16 Weighting of index numbers 156 Weighting of results 48, 156 Weights 26, 48, 156 What if 16, 26 Why technique 35 Wilcoxon test 3 18ff.

Yield 445

Zero matrix 579