## Business Statistics Abridged: Australia and New Zealand, 8th Edition

By Eliyathamby A Selvanathan, Saroja Selvanathan and Gerald Keller

Contents

Preface XII

Guide to the text XVI

Guide to the online Resources XX

Acknowledgement XXII

About the Authors XXIII

1 What is statistics? 1

Introduction to statistics 2

1.1 Key statistical concepts 5

1.2 Statistical applications in business 6

Case 3.6 Differing average weekly earnings of men and women in Australia 7

Case 4.2 Analysing the spread of the Global Coronavirus Pandemic 7

Case 5.5 Sydney and Melbourne lead the way in the growth in house prices 7

Case 14.1 Comparing salary offers for finance and marketing MBA majors – I 8

Case 16.1 Gold lotto 8

Case 17.3 Does unemployment affect inflation in New Zealand? 9

1.3 How managers use statistics 9

1.4 Statistics and the computer 11

1.5 Online resources 13

Appendix 1.A Introduction to Microsoft Excel 15

2 Types of data, data collection and sampling 18

Introduction 19

2.1 Types of data 20

2.2 Methods of collecting data 26

2.3 Sampling 30

2.4 Sampling plans 32

2.5 Sampling and non-sampling errors 39

Chapter summary 41

PART 1: DESCRIPTIVE MEASURES AND PROBABILITY 43

3 Graphical descriptive techniques – Nominal data 44

Introduction 45

3.1 **Graphical techniques** to describe nominal data 46

3.2 Describing the relationship between two nominal variables 68

Chapter summary 74

Case 3.1 Analysing the COVID-19 deaths in Australia by gender and age group 77

Case 3.2 Corporate tax rates around the world 77

Case 3.3 Trends in CO2 emissions 78

Case 3.4 Where is the divorce rate heading? 79

Case 3.5 Geographic location of share ownership in Australia 80

Case 3.6 Differing average weekly earnings of men and women in Australia 80

Case 3.7 The demography of Australia 81

Case 3.8 Survey of graduates 82

Case 3.9 Analysing the health effect of the Coronavirus pandemic 82

Case 3.10 Australian domestic and overseas student market by states and territories 82

Case 3.11 Road fatalities in Australia 83

Case 3.12 Drinking behaviour of Australians 84

4 Graphical descriptive techniques – Numerical data 85

Introduction 86

4.1 Graphical techniques to describe numerical data 86

4.2 Describing time-series data 106

4.3 Describing the relationship between two or more numerical variables 111

4.4 Graphical excellence and deception 123

Chapter summary 131

Case 4.1 The question of global warming 133

Case 4.2 Analysing the spread of the global coronavirus pandemic 134

Case 4.3 An analysis of telephone bills 134

Case 4.4 An analysis of monthly retail turnover in Australia 134

Case 4.5 Economic freedom and prosperity 134

5 Numerical descriptive measures 135

Introduction 136

5.1 Measures of central location 136

5.2 Measures of variability 153

5.3 Measures of relative standing and box plots 169

5.4 Measures of association 179

5.5 General guidelines on the exploration of data 193

Chapter summary 195

Case 5.1 Return to the global warming question 199

Case 5.2 Another return to the global warming question 199

Case 5.3 GDP versus consumption 199

Case 5.4 The gulf between the rich and the poor 199

Case 5.5 Sydney and Melbourne leading the way in the growth in house prices 200

Case 5.6 Performance of managed funds in Australia: 3-star, 4-star and

5-star rated funds 200

Case 5.7 Life in suburbs drives emissions higher 201

Case 5.8 Aussies and Kiwis are leading in education 202

Case 5.9 Growth in consumer prices and consumption in Australian states 202

Appendix 5.A Summation notation 203

Appendix 5.B Descriptive measures for grouped data 206

6 Probability 211

Introduction 212

6.1 Assigning probabilities to events 212

6.2 Joint, marginal and conditional probability 224

6.3 Rules of probability 234

6.4 Probability trees 239

6.5 Bayes’ law 244

6.6 Identifying the correct method 251

Chapter summary 252

Case 6.1 Let’s make a deal 255

Case 6.2 University admissions in Australia: Does gender matter? 255

Case 6.3 Maternal serum screening test for Down syndrome 255

Case 6.4 Levels of disability among children in Australia 256

Case 6.5 Probability that at least two people in the same room have the same birthday 257

Case 6.6 Home ownership in Australia 257

Case 6.7 COVID-19 confirmed cases and deaths in Australia II 259

7 Random variables and discrete probability distributions 260

Introduction 261

7.1 Random variables and probability distributions 261

7.2 Expected value and variance 269

7.3 Binomial distribution 275

7.4 Poisson distribution 284

7.5 Bivariate distributions 290

7.6 Applications in finance: Portfolio diversification and asset allocation 296

Chapter summary 303

Case 7.1 Has there been a shift in the location of overseas-born population

within Australia over the 50 years from 1996 to 2016? 306

Case 7.2 How about a carbon tax on motor vehicle ownership? 306

Case 7.3 How about a carbon tax on motor vehicle ownership? – New Zealand 307

Case 7.4 Internet usage by children 307

Case 7.5 COVID-19 deaths in Australia by age and gender III 308

8 Continuous probability distributions 309

Introduction 310

8.1 Probability density functions 310

8.2 Uniform distribution 313

8.3 Normal distribution 316

8.4 Exponential distribution 336

Chapter summary 341

Case 8.1 Average salary of popular business professions in Australia 343

Case 8.2 **Fuel consumption** of popular brands of motor vehicles 343

Appendix 8.A Normal approximation to the binomial distribution 344

PART 2: STATISTICAL INFERENCE 349

9 Statistical inference and sampling distributions 350

Introduction 351

9.1 Data type and problem objective 351

9.2 Systematic approach to statistical inference: A summary 352

9.3 Introduction to sampling distribution 354

9.4 Sampling distribution of the sample mean X — 354

9.5 Sampling distribution of the sample proportion ˆp 366

9.6 From here to inference 369

Chapter summary 371

10 Estimation: Single population 373

Introduction 374

10.1 Concepts of estimation 375

10.2 Estimating the population mean μ when the population variance σ 2 is known 378

10.3 Estimating the population mean μ when the population variance σ2 is unknown 391

10.4 Estimating the population proportion p 403

10.5 Determining the required sample size 410

10.6 Applications in marketing: Market segmentation 417

Chapter summary 422

Case 10.1 Estimating the monthly average petrol price in Queensland 426

Case 10.2 Cold men and cold women will live longer! 426

Case 10.3 Super fund managers letting down retirees 427

Appendix 10.A Excel instructions for missing data and for recoding data 428

11 Estimation: Two populations 429

Introduction 430

11.1 Estimating the difference between two population means (μ1 − μ2) when the

population variances are known: Independent samples 431

11.2 Estimating the difference between two population means (μ1 − μ2) when

the population variances are unknown: Independent samples 439

11.3 Estimating the difference between two population means with matched pairs

experiments: Dependent samples 449

11.4 Estimating the difference between two population proportions, p1 – p2 453

Chapter summary 461

Case 11.1 Has demand for print newspapers declined in Australia? 463

Case 11.2 Hotel room prices in Australia: Are they becoming cheaper? 463

Case 11.3 Comparing hotel room prices in New Zealand 464

Case 11.4 Comparing salary offers for finance and marketing major graduates 464

Case 11.5 Estimating the cost of a life saved 465

12 Hypothesis testing: Single population 466

Introduction 467

12.1 Concepts of hypothesis testing 467

12.2 Testing the population mean μ when the population variance σ 2 is known 476

12.3 The p-value of a test of hypothesis 491

12.4 Testing the population mean μ when the population variance σ 2 is unknown 504

12.5 Calculating the probability of a Type II error 510

12.6 Testing the population proportion p 517

Chapter summary 524

Case 12.1 Singapore Airlines has done it again 527

Case 12.2 Australian rate of real unemployment 527

Case 12.3 The republic debate: What Australians are thinking 527

Case 12.4 Has Australian Business Confidence improved since the May 2019 election? 528

Case 12.5 Is there a gender bias in the effect of COVID-19 infection? 528

Appendix 12.A Excel instructions 529

13 Hypothesis testing: Two populations 530

Introduction 531

13.1 Testing the difference between two population means: Independent samples 531

13.2 Testing the difference between two population means: Dependent

samples – matched pairs experiment 551

13.3 Testing the difference between two population proportions 562

Chapter summary 573

Case 13.1 Is there gender difference in spirits consumption? 578

Case 13.2 Consumer confidence in New Zealand 578

Case 13.3 New Zealand Government bond yields: Short term versus long term 579

Case 13.4 The price of petrol in Australia: Is it similar across regions? 579

Case 13.5 Student surrogates in market research 579

Case 13.6 Do expensive drugs save more lives? 580

Case 13.7 Comparing two designs of ergonomic desk: Part I 580

Appendix 13.A Excel instructions: Manipulating data 581

14 Chi-squared tests 582

Introduction 583

14.1 Chi-squared goodness-of-fit test 583

14.2 Chi-squared test of a contingency table 593

14.3 Chi-squared test for normality 608

14.4 Summary of tests on nominal data 614

Chapter summary 616

Case 14.1 Gold lotto 620

Case 14.2 Exit polls 620

Case 14.3 How well is the Australian Government managing the coronavirus pandemic? 620

Appendix 14.A Chi-squared distribution 622

15 Simple linear regression and correlation 624

Introduction 625

15.1 Model 626

15.2 Estimating the coefficients 628

15.3 Error variable: Required conditions 641

15.4 Assessing the model 643

15.5 Using the regression equation 659

15.6 Testing the coefficient of correlation 664

15.7 Regression diagnostics – I 667

Chapter summary 677

Case 15.1 Does unemployment rate affect weekly earnings in New Zealand? 683

Case 15.2 Tourism vs tax revenue 683

Case 15.3 Does unemployment affect inflation in

New Zealand? 683

Case 15.4 Does domestic market capital influence stock prices? 683

Case 15.5 Book sales vs free examination copies 683

Case 15.6 Does increasing per capita income lead to increase in energy consumption? 684

Case 15.7 Market model of share returns 684

Case 15.8 Life insurance policies 685

Case 15.9 Education and income: How are they related? 685

Case 15.10 Male and female unemployment rates in

New Zealand – Are they related? 685

16 Multiple regression 686

Introduction 687

16.1 Model and required conditions 687

16.2 Estimating the coefficients and assessing the model 688

16.3 Regression diagnostics – II 714

16.4 Regression diagnostics – III (time series) 726

Chapter summary 736

Case 16.1 Are lotteries a tax on the poor and uneducated? 741

Case 16.2 Demand for beer in Australia 741

Case 16.3 Book sales vs free examination copies revisited 741

Case 16.4 Average hourly earnings in New Zealand 742

Case 16.5 Testing a more effective device to keep arteries open 742

Appendix 16.A F-distribution 743

PART 3: APPLICATIONS 747

17 Time series analysis and forecasting 748

Introduction 749

17.1 Components of a time series 749

17.2 Smoothing techniques 753

17.3 Trend analysis 763

17.4 Measuring the cyclical effect 768

17.5 Measuring the seasonal effect 772

17.6 Introduction to forecasting 780

17.7 Time series forecasting with exponential smoothing 783

17.8 Time series forecasting with regression 785

Chapter summary 796

Case 17.1 Part-time employed females 798

Case 17.2 New Zealand tourism: Tourist arrivals 798

Case 17.3 Seasonal and cyclical effects in number of houses constructed in Queensland 798

Case 17.4 Measuring the cyclical effect on Woolworths‘ stock prices 798

18 Index numbers 799

Introduction 800

18.1 Constructing unweighted index numbers 801

18.2 Constructing weighted index numbers 808

18.3 The Australian Consumer Price Index (CPI) 812

18.4 Using the CPI to deflate wages and GDP 816

18.5 Changing the base period of an index number series 821

Chapter summary 824

Case 18.1 Soaring petrol prices in Australian capital cities 828

Case 18.2 Is the Australian road toll on the increase again? 828

A : Summary Solutions For Selected

(Even-Numbered) Exercises 829

Appendix B : Statistical Tables 8 4 3

Glossary 864

Index 869