# A Guide to Business Statistics

• ID: 4454874
• Book
• 208 Pages
• John Wiley and Sons Ltd
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An accessible text that explains fundamental concepts in business statistics that are often obscured by formulae and mathematical notation

A Guide to Business Statistics offers a practical approach to statistics that covers the fundamental concepts in business and economics. The book maintains the level of rigor of a more conventional textbook in business statistics but uses a more streamlined and intuitive approach. In short, A Guide to Business Statistics provides clarity to the typical statistics textbook cluttered with notation and formulae.

The author an expert in the field offers concise and straightforward explanations to the core principles and techniques in business statistics. The concepts are introduced through examples, and the text is designed to be accessible to readers with a variety of backgrounds. To enhance learning, most of the mathematical formulae and notation appears in technical appendices at the end of each chapter. This important resource:

• Offers a comprehensive guide to understanding business statistics targeting business and economics students and professionals
• Introduces the concepts and techniques through concise and intuitive examples
• Focuses on understanding by moving distracting formulae and mathematical notation to appendices
• Offers intuition, insights, humor, and practical advice for students of business statistics
• Features coverage of sampling techniques, descriptive statistics, probability, sampling distributions, confidence intervals, hypothesis tests, and regression

Written for undergraduate business students, business and economics majors, teachers, and practitioners, A Guide to Business Statistics offers an accessible guide to the key concepts and fundamental principles in statistics.

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Preface xiii

1 Types of Data 1

1.1 Categorical Data 2

1.2 Numerical Data 3

1.3 Level of Measurement 4

1.4 Cross–Sectional, Time–Series, and Panel Data 5

1.5 Summary 7

2 Populations and Samples 9

2.1 What is the Population of Interest? 10

2.2 How to Sample From a Population? 11

2.2.1 Simple Random Sampling 11

2.2.2 Stratified Sampling 14

2.2.3 Other Methods 15

2.3 Getting the Data 16

2.4 Summary 17

3 Descriptive Statistics 19

3.1 Measures of Central Tendency 20

3.1.1 The Mean 20

3.1.2 The Median 23

3.1.3 The Mode 24

3.2 Measures of Variability 24

3.2.1 Variance and Standard Deviation 24

3.3 The Shape 26

3.4 Summary 28

Technical Appendix 29

4 Probability 31

4.1 Simple Probabilities 32

4.1.1 When to Add Probabilities Together 34

4.1.2 When to Find Intersections 36

4.2 Empirical Probabilities 37

4.3 Conditional Probabilities 39

4.4 Summary 41

Technical Appendix 42

5 The Normal Distribution 43

5.1 The Bell Shape 43

5.2 The Empirical Rule 44

5.3 Standard Normal Distribution 46

5.3.1 Probabilities with Continuous Distributions 48

5.3.2 Verifying the Empirical Rule Using the z–table 48

5.4 Normal Approximations 48

5.4.1 Mean 49

5.4.2 Standard deviation 49

5.4.3 Shape 50

5.5 Summary 51

Technical Appendix 52

6 Sampling Distributions 55

6.1 Defining a Sampling Distribution 55

6.2 The Importance of Sampling Distributions 56

6.3 An Example of a Sampling Distribution 57

6.4 Characteristics of a Sampling Distribution of a Mean 61

6.4.1 The Mean 61

6.4.2 The Shape 62

6.4.3 The Standard Deviation 64

6.4.4 Finding Probabilities With a Sampling Distribution 65

6.5 Sampling Distribution of a Proportion 67

6.5.1 The Mean 68

6.5.2 The Shape 68

6.5.3 The Standard Deviation 68

6.6 Summary 70

Technical Appendix 71

7 Confidence Intervals 73

7.1 Confidence Intervals for Means 74

7.1.1 The Characteristics of the Sampling Distribution 75

7.1.2 Confidence Intervals Using the z–Distribution 76

7.1.3 Confidence Intervals Using the t–Distribution 78

7.2 Confidence Intervals for Proportions 80

7.3 Sample Size and theWidth of Confidence Intervals 81

7.4 Comparing Two Proportions From the Same Poll 82

7.5 Summary 84

Technical Appendix 85

8 Hypothesis Tests of a Population Mean 89

8.1 Two–Tail Hypothesis Test of a Mean 90

8.1.1 A Single Sample from a Population 90

8.1.2 Setting Up the Null and Alternative Hypothesis 92

8.1.3 Decisions and Errors 92

8.1.4 Rejection Regions and Conclusions 94

8.1.5 Changing the Level of Significance 95

8.2 One–Tail Hypothesis Test of a Mean 97

8.2.1 Setting Up the Null and Alternative Hypotheses 97

8.2.2 Rejection Regions and Conclusions 98

8.3 p–Value Approach to Hypothesis Tests 99

8.3.1 One–Tail Tests 99

8.3.2 Two–tail tests 100

8.4 Summary 100

Technical Appendix 101

9 Hypothesis Tests of Categorical Data 103

9.1 Two–Tail Hypothesis Test of a Proportion 104

9.1.1 A Single Sample from a Population 104

9.1.2 Rejection Regions and Conclusions 106

9.2 One–Tail Hypothesis Test of a Proportion 107

9.3 Using p–Values 108

9.3.1 One–Tail Tests Using the p–Value 108

9.3.2 Two–Tail Tests Using the p–Value 108

9.4 Chi–Square Tests 109

9.4.1 The Data in a Contingency Table 109

9.4.2 Chi–Square Test of Goodness of Fit 111

9.5 Summary 114

Technical Appendix 115

10 Hypothesis Tests Comparing Two Parameters 117

10.1 The Approach in this Chapter 118

10.2 Hypothesis Tests of Two Means 118

10.2.1 The Null and Alternative Hypothesis 118

10.2.2 t–Test Assuming Equal Variances 121

10.2.3 t–Test Assuming Unequal Variances 122

10.2.4 One–Tail Hypothesis Tests of Two Means 124

10.2.5 A Note on Hypothesis Tests Using Paired Observations 124

10.3 Hypothesis Tests of Two Variances 126

10.4 Hypothesis Tests of Two Proportions 128

10.5 Summary 130

Technical Appendix 131

11 Simple Linear Regression 133

11.1 The Population Regression Model 134

11.2 A Look at the Data 135

11.3 Ordinary Least Squares (OLS) 137

11.4 The Distribution of b0 and b1 139

11.5 Tests of Significance 140

11.6 Goodness of Fit 142

11.7 Checking for Violations of the Assumptions 143

11.7.1 The Normality Assumption 143

11.7.2 The Constant Variance Assumption 144

11.8 Summary 146

Technical Appendix 147

12 Multiple Regression 149

12.1 Population Regression Model 149

12.2 The Data 150

12.3 Sample Regression Function 151

12.4 Interpreting the Estimates 152

12.4.1 Attendance 153

12.4.2 SAT 153

12.4.3 Hours Studying 153

12.4.4 Logic Test 153

12.4.5 Female 153

12.4.6 Senior 154

12.5 Prediction 154

12.6 Tests of Significance 154

12.6.1 Joint Hypothesis Test 155

12.7 Goodness of Fit 156

12.8 Multicollinearity 157

12.8.1 Variance Inflation Factor (VIF) 157

12.8.2 An Example of Violating the Assumption of no Multicollinearity 159

12.9 Summary 162

Technical Appendix 163

13 More Topics in Regression 165

13.1 Hypothesis Tests Comparing Two MeansWith Regression 165

13.2 Hypothesis Tests Comparing MoreThan Two Means (ANOVA) 168

13.3 Interacting Variables 170

13.3.1 Gender Differences in StartingWages 171

13.3.2 Gender Differences inWage Increase from Experience 172

13.4 Nonlinearities 173

13.5 Time–Series Analysis 175

13.6 Summary 177

Index 179

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