# A Guide to Business Statistics

By: David M. McEvoy (author)Paperback

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DAVID M. MCEVOY, PHD, is an Associate Professor in the Economics Department at Appalachian State University in Boone NC. He has published over 20 peer-reviewed articles and is coeditor of two books. Dr. McEvoy is an award-winning educator who has taught undergraduate courses in business statistics for over 10 years.

### Contents

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

### Product Details

• ISBN13: 9781119138358
• Format: Paperback
• Number Of Pages: 208
• ID: 9781119138358
• weight: 344
• ISBN10: 1119138353

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