Chapter 0 A refresher in basic mathematics 1
1 Self-check tests 2
2 Basic arithmetic 10
3 Use of powers 14
4 Basic algebra 16
5 Graphs and more algebra 18
6 Use of calculators 25
7 Answers to recheck tests 30
Part 1 Quantitatlv? Information 37
Chapter 1 Data collection 43
1.1 Population 44
1.2 Sources of data 46
1.3 Secondary data 46
1.4 Primary data collection 48
1.5 Asking questions 54
1.6 Non-response to surveys 61
1.7 Some alternative methods 62
1.8 Market research 63
1.9 Types of data 64
1.10 Conclusions 65
1．11 Problems 67
Chapter 2 Presentation of data 70
2.1 Tabulation of data 71
2.2 Visual presentation 75
2.3 Graphical representation 85
2.4 Conclusions 91
2.5 Problems 91
Part 1 Conclusions 97
Part 2 Descriptive statisties 99
3.1 The mean,median and mode 101
Chapter 3 Measures of location 101
3.2 Other measures of location 112
3.3 Conclusions 115
3.4 Problems 116
Chapter 4 Measures of dispersion 120
4.1 The standard devlation 120
4.2 Other measures of dispersion 126
4.3 Relative measures of dispersion 130
4.4 Variability in sample data 131
4.5 Conclusions 134
4.6 Problems 134
4.7 Appendix 139
Chapter 5 Index numbers 140
5.1 The interpretation of an index number 140
5.2 The construction of index numbers 146
5.3 The weighting of index numbers 151
5.4 The General Index of Retail Prices 153
5.5 Conclusions 155
5.6 Problems 156
Part 2 Conclusions 160
Part 3 Measuring uncertainty 161
Chapter 6 Probability 163
6.1 Basic concepts 164
6.2 Definitions 166
6.3 Basic relationships in probability 168
6.4 Probability trees 172
6.5 Expected values 173
6.6 Decision trees 175
6.7 Bayes Theorem 176
6.8 Markov Chains 178
6.9 Conclusions 181
6.10 Problems 182
Chapter 7 Discrete probability distributions 189
7.1 Uniform distribution 190
7.2 Binomial distribution 191
7.3 Poisson distribution 197
7.4 Poisson approximation to the Binomial 199
7.5 Conclusions 199
7.6 Problems 200
Chapter 8 The Normal distribution 203
8.1 Characteristics of the Normal distribution 203
8.2 The standard Normal distribution 204
8.3 Normal approximation to the Binomial 208
8.4 Normal approximation to the Poisson 210
8.5 Combinations of varlables 211
8.6 Central Limit Theorem 213
8.7 Conclusions 217
8.8 Problems 217
Part 3 Conclusions 221
Part 4 Statistical inference 223
Chapter 9 Confidence intervals 227
9.1 Statistical inference 228
9.2 Inference on the population mean 229
9.3 Inference on the population percentage 237
9.4 The difference between independent samples 240
9.5 The finite population correction factor 243
9.6 The t-distribution 245
9.7 Confidence interval for the median-large sample approximation 249
9.9 Problems 251
9.8 Conclusions 251
Chapter 10 Significance testing 257
10.1 Significance testing using confidence intervals 258
10.2 Hypothesis testing for single samples 259
10.3 One-sided significance tests 265
10.4 Types of error 270
10.5 Hypothesis testing with two samples 273
10.6 Hypothesis testing with small samples 276
10.7 Conclusions 281
10.8 Problems 282
Chapter 11 Non-parametric tests 286
11.1 Chi-squared tests 287
11.2 Mann-Whitney U test 301
11.3 Wilcoxon test 304
11.4 Runs test 307
11.5 Conclusions 308
11.6 Problems 309
Part 4 Conclusions 316
Part 5 Relating variables and predicting outcomes 317
Chapter 12 Time series 319
12.1 Time series models 321
12.2 The trend 324
12.3 The seasonal factors 333
12.4 The cyclical factors 338
12.5 The residual or random factor 339
12.6 Predictions 340
12.7 Exponentially weighted moving averages 343
12.8 Summary and conclusions 345
12.9 Problems 347
Chapter 13 Correlation 352
13.1 Scatter diagrams 353
13.2 Cause and effect relationships 355
13.3 Measuring linear association 358
13.4 The coefficient of determination 362
13.5 Measuring non-linear association 364
13.6 Testing the significance of the correlation 367
13.7 Conclusions 370
13.8 Problems 370
13.9 Derivation of the correlation coefficient 376
13.10 Algebraic link between Spearman s and Pearson s coefficients 376
Chapter 14 Regression 378
14.1 Linear regression 379
14.2 The graph of the regression line 381
14.3 Predictions from the regression line 382
14.4 Another regression line 387
14.5 Interpretation 388
14.6 Non-linear relationships 389
14.7 Conclusions 390
14.8 Problems 390
14.9 Appendix 394
Chapter 15 Multiple regression and correlation 397
15.1 The basic two-variable model 398
15.2 The effects of adding variables 401
15.3 Assumptions and econometric problems 404
15.4 Analysis of a multiple regression model 409
15.5 Using multiple regression models 413
15.6 Conclusions 414
15.7 Problems 414
Part 5 Conclusions 420
Part 6 Modelling 423
Chapter 16 The time value of money 425
16.1 Interest:simple and compound 426
16.2 Depreciation 429
16.3 Present value 431
16.4 The internal rate of return 434
16.5 Incremental payments 438
16.6 Annual percentage rate(APR) 441
16.7 Conclusions 442
16.8 Problems 444
16.9 Appendix 446
Chapter 17 Linear programming 448
17.1 Definition of a feasible area 449
17.2 The solution of a linear programming problem 450
17.3 Special cases 456
17.4 The value of resources 459
17.5 Computer-based solutions 461
17.7 Problems 467
17.6 Conclusions 467
Chapter 18 Networks 473
18.1 Notation and construction 474
18.2 The critical path 477
18.3 Measures of float 479
18.4 Gantt charts and managing resources 481
18.5 Project time reduction 482
18.6 Uncertainty 486
18.7 Conclusions 487
18.8 Problems 487
Chapter 19 Modelling stock control and queues 493
19.1 Introduction to the economic order quantity model 493
19.2 Quantity discounts 498
19.3 Non-zero lead time 499
19.4 Introduction to modelling queues 502
19.5 A model for a single queue 503
19.6 Queues - modelling cost 505
19.7 Modelling multi-channel queues 507
19.8 Conclusions 509
19.9 Problems 510
19.10 Appendix - proof of EBQ 511
Chapter 20 Simulation 513
20.1 An introduction to simulation models 514
20.2 Developing a simple simulation model 515
20.3 Random event generation 516
20.4 The construction of a simulation model 520
20.5 Conclusions 521
20.6 Problems 521
Part 6 Conclusions 523
Part 7 Mathematical background 525
Chapter 21 Mathematical relationships 527
21.1 Introduction to algebra 528
21.2 Powers 531
21.3 Arithmetic and geometric progressions 532
21.4 Functions 536
21.5 Conclusions 551
21.6 Problems 551
21.7 Proof of AP 554
21.8 Proof of GP 554
21.9 Proof of quadratic formula 555
Chapter 22 Matrices 556
22.1 What is a matrix? 557
22.2 Matrix manipulation 557
22.3 Solutions of simultaneous equations 566
22.4 Leontief input-output analysis 570
22.5 Conclusions 573
22.6 Problems 574
Chapter 23 Use of calculus 577
23.1 Differentiation 577
23.2 Economic applicationsⅠ 584
23.3 Turning points 587
23.4 Economic applicationsⅡ 590
23.5 Further notes 591
23.6 Integration 594
23.7 Economic summary 597
23.8 Functions of more than one variable 597
23.9 Maximization and minimization subject to constraints 601
23.10 Conclusions 603
23.11 Problems 604
Part 7 Conclusions 609
Typical examination questions 611
Appendices 618
A Cumulative Binomial probabilities 618
B Cumulative Poisson probabilities 619
C Areas in the right-hand tail of the Normal distribution 620
D Student s t critical points 622
E χ2 critical values 624
F Present value factors 626
G Mann-Whitney test statistic 628
H Wilcoxon test statistic 631
I Runs test 632
J Durbin-Watson statistic 634
K Random number table 636
L Loading MICROSTATS 638
Answers to selected problems 640
Index 661