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Applied statistics for business and economics

Author: Leekley, Robert M. Publisher: CRC Press, 2010.Language: EnglishDescription: 476 p. : Graphs ; 26 cm.ISBN: 9781439805688Type of document: BookBibliography/Index: Includes index
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Book Europe Campus
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Print HA29 .L44 2009
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001271676
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Includes index

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Applied Statistics for Business and Economics Contents Preface ..................................................................................................................... xiii Acknowledgments.................................................................................................... xvii Author....................................................................................................................... xix 1 Introduction to Statistics ................................................................................. 1 1.1 What Is Statistics Good For? 1 1.2 Some Further Applications of Statistics 3 1.2.1 Statistics in the Real World 4 1.2.1.1 Quality Assurance 4 1.2.1.2 Auditing 4 1.2.1.3 Market Research 5 1.2.1.4 Political Polling 5 1.2.1.5 Social Science Research 6 1.2.2 Statistics in the Classroom 6 1.2.2.1 Party Control and the Taxation of the Rich 6 1.2.2.2 Racial Discrimination in Major League Baseball: Can It Exist When Productivity Is Crystal Clear? 7 1.2.2.3 The Campus Bookstore: Perceptions and Solutions 8 1.3 Some Basic Statistical Ideas 9 1.3.1 Description and Inference 9 1.3.2 Explanation and Causation 10 1.3.3 The Population and the Sample 11 1.3.4 Variables and Cases 11 1.3.5 Types of Variables 11 1.3.5.1 Numerical and Categorical Variables 11 1.3.5.2 Discrete and Continuous Numerical Variables 12 1.3.6 Sampling Error and Bias 12 1.4 On Studying Statistics 13 Describing Data: Tables and Graphs .............................................................. 15 2.1 Looking at a Single Variable 15 2.1.1 Frequency Distributions 15 2.1.1.1 Ordinary Frequency Distributions 15 2.1.1.2 Relative Frequency Distributions 18 2.1.1.3 Cumulative Frequency Distributions 19 2.1.2 Graphs 21 2.1.2.1 Bar Charts and Pie Charts 21 2.1.2.2 Histograms 22 2 2.2 2.3 2.4 3 Looking for Relationships 23 2.2.1 Categorical Explanatory Variables 23 2.2.1.1 Frequency Distributions 23 2.2.1.2 Graphs 25 2.2.1.3 A More Interesting Example 27 2.2.1.4 Frequency Polygons 31 2.2.1.5 Scattergrams 33 2.2.2 Continuous Explanatory Variables 35 2.2.2.1 Frequency Distributions 35 2.2.2.2 Scattergrams 36 Looking at Variables over Time 37 Exercises 39 Describing Data: Summary Statistics............................................................. 43 3.1 When Pictures Will Not Do 43 3.2 Measures of a Single Numeric Variable 43 3.2.1 Measures of Central Tendency 43 3.2.1.1 The Arithmetic Mean 44 3.2.1.2 The Median 46 3.2.1.3 The Mode 47 3.2.1.4 A More Interesting Example 47 3.2.1.5 From a Frequency Distribution 47 3.2.1.6 Working from Grouped Data 49 3.2.2 Measures of Variation 51 3.2.2.1 The Range 51 3.2.2.2 The Variance 52 3.2.2.3 The Standard Deviation 54 3.2.2.4 The Coefficient of Variation 54 3.2.2.5 A More Interesting Example 55 3.2.2.6 Making Sense of the Standard Deviation: The Empirical Rule 55 3.2.2.7 From a Frequency Distribution 57 3.2.2.8 Working from Grouped Data 58 3.2.3 Spreadsheet Statistical Functions 59 3.2.4 Summing Up 60 3.3 Measures of a Single Categorical Variable 61 3.4 Measures of a Relationship 62 3.4.1 Categorical Explanatory Variables 62 3.4.1.1 Comparing Proportions 62 3.4.1.2 Comparing Means 64 3.4.2 Continuous Explanatory Variables* 65 3.5 Exercises 68 Basic Probability............................................................................................. 71 4.1 Why Probability? 71 4.2 The Basics 71 4.2.1 Experiments and Events 71 4.2.2 Discrete versus Continuous Probabilities 72 4 4.3 4.4 4.5 4.6 5 4.2.3 The Probability of an Event 72 4.2.4 Complementary Events 74 4.2.5 Conditional Probabilities 74 4.2.6 Independent Events 75 4.2.7 Mutually Exclusive Events 76 Computing Probabilities 77 4.3.1 The Probability of an Intersection 77 4.3.1.1 The General Case 77 4.3.1.2 A Special Case: Independent Events 79 4.3.2 The Probability of a Union 80 4.3.2.1 The General Case 80 4.3.2.2 A Special Case: Mutually Exclusive Events 80 Some Tools That May Help 81 4.4.1 Two-Way Tables 81 4.4.2 Tree Diagrams 83 Revising Probabilities with Bayes' Theorem 88 Exercises 91 Probability Distributions.............................................................................. 95 5.1 Discrete Random Variables 95 5.1.1 Discrete Random Variables and Probability Distributions 95 5.1.2 The Mean and Standard Deviation of a Probability Distribution 96 5.1.3 Special Cases 97 5.2 The Binomial Probability Distribution 98 5.2.1 The Binomial Formula 98 5.2.1.1 The Probability of a Single Branch of a Tree 98 5.2.1.2 The Number of Branches: Combinations 99 5.2.1.3 Putting It All Together 100 5.2.2 Aids in Finding Binomial Probabilities 102 5.2.2.1 The Binomial Table 103 5.2.2.2 The Binomial Spreadsheet Functions 103 5.2.3 The Mean and Standard Deviation of the Binomial Distribution 104 5.3 Continuous Random Variables 105 5.4 The Normal Distribution: The Bell-Shaped Curve 106 5.4.1 The Standard Normal Distribution 107 5.4.1.1 The Standard Normal Table 107 5.4.1.2 The Standard Normal Spreadsheet Functions 110 5.4.1.3 Two Final Points 110 5.4.2 Standardizing a Normal Distribution 110 5.5 The Normal Approximation to the Binomial 114 5.6 Exercises 118 Sampling and Sampling Distributions ........................................................ 121 6.1 Sampling* 121 6.1.1 Random and Judgment Samples 121 6 6.1.2 6.2 6.3 6.4 6.5 6.6 6.7 7 Techniques for Random Sampling 122 6.1.2.1 Random Number Tables 122 6.1.2.2 Random Number Generators 123 6.1.2.3 Systematic Random Sampling 123 6.1.3 More Advanced Techniques 124 6.1.3.1 Stratified Sampling 124 6.1.3.2 Cluster Sampling 125 What Are Sampling Distributions and Why Are They Interesting? 125 The Sampling Distribution of a Proportion 126 6.3.1 Three Complications 131 The Sampling Distribution of a Mean: cx Known 133 6.4.1 Two Complications 139 The Sampling Distribution of a Mean: cx Unknown 140 6.5.1 The t Table 141 6.5.2 The t Spreadsheet Functions 142 Other Sampling Distributions 147 Exercises 147 Estimation and Confidence Intervals ........................................................... 151 7.1 Point and Interval Estimators of Unknown Population Parameters 151 7.1.1 Qualities of a Good Point Estimator 151 7.1.1.1 Unbiasedness 152 7.1.1.2 Efficiency 152 7.1.2 Point versus Interval Estimators 152 7.2 Estimates of the Population Proportion 154 7.3 Estimates of the Population Mean 157 7.4 A Final Word on Confidence Intervals 161 7.5 Exercises 162 Tests of Hypotheses: One-Sample Tests....................................................... 167 8.1 Testing a Claim: Type I and Type II Errors 167 8.2 A Two-Tailed Test for the Population Proportion 168 8.2.1 The Null and Alternative Hypotheses 168 8.2.2 The Decision Criterion: Setting the Probability of a Type I Error 168 8.2.3 The Calculations 170 8.2.4 The Conclusion 170 8.2.5 The P-Value of the Test 172 8.2.6 The Probability of a Type II Error* 173 8.3 A One-Tailed Alternative for the Population Proportion 179 8.3.1 The Null and Alternative Hypotheses 180 8.3.2 The Decision Criterion 181 8.3.3 The Probability of a Type II Error* 184 8.3.4 When a One-Tailed Test is Legitimate 185 8.4 Tests for the Population Mean 186 8.5 A Two-Tailed Test for the Population Mean 187 8.5.1 The Null and Alternative Hypotheses 187 8.5.2 The Decision Criterion 187 8 8.6 8.7 8.8 8.5.3 The Calculations 189 8.5.4 The Conclusion 190 8.5.5 The P-Value of the Test 190 8.5.6 The Probability of a Type II Error* 192 A One-Tailed Alternative for the Population Mean 195 8.6.1 The Null and Alternative Hypotheses 195 8.6.2 The Decision Criterion 195 8.6.3 The Probability of a Type II Error* 197 A Final Word on One-Sample Tests 198 Exercises 198 9 Tests of Hypotheses: Two-Sample Tests........................................................... 203 9.1 Looking for Relationships Again 203 9.2 A Difference in Population Proportions 205 9.2.1 The Null and Alternative Hypotheses 205 9.2.2 The Decision Criterion 207 9.2.3 The Calculations 208 9.2.4 The Conclusion 209 9.3 A Difference in Population Means 212 9.4 A Difference in Means: axs Known 212 9.4.1 The Null and Alternative Hypotheses 212 9.4.2 The Decision Criterion 212 9.4.3 The Formulas 213 9.5 A Difference in Means: axs Unknown but Equal 213 9.5.1 The Null and Alternative Hypotheses 213 9.5.2 The Decision Criterion 214 9.5.3 The Calculations 214 9.5.4 The Conclusion 215 9.6 A Difference in Means: o-xs Unknown and Unequal* 217 9.7 A Difference in Means: Using Paired Data* 221 9.8 A Final Word on Two-Sample Tests 223 9.9 Exercises 224 10 Tests of Hypotheses: Contingency and Goodness-of-Fit .................................. 229 10.1 A Difference in Proportions: An Alternate Approach 230 10.1.1 The Null and Alternative Hypotheses 230 10.1.2 The Decision Criterion 230 10.1.3 The Calculations 231 10.1.4 The Conclusion 233 10.2 Contingency Tables with Several Rows and/or Columns 233 10.3 A Final Word on Contingency Tables 237 10.4 Testing for Goodness-of-Fit 238 10.4.1 The Null and Alternative Hypotheses 238 10.4.2 The Decision Criterion 239 10.4.3 The Calculations 239 10.4.4 The Conclusion 239 10.5 A Final Example on Testing for Goodness-of-Fit 242 10.6 Exercises 245 11 Tests of Hypotheses: ANOVA and Tests of Variances ........................................ 249 11.1 A Difference in Means: An Alternate Approach 250 11.1.1 The Null and Alternative Hypotheses 250 11.1.2 The Decision Criterion 250 11.1.3 The Calculations 251 11.1.4 The Conclusion 253 11.2 ANOVA with Several Categories 254 11.3 A Final Word on ANOVA 258 11.4 A Difference in Population Variances 259 11.4.1 The Null and Alternative Hypotheses 260 11.4.2 The Decision Criterion 260 11.4.3 The Calculations 261 11.4.4 The Conclusion 261 11. 5 Exercises 263 12 Simple Regression and Correlation ................................................................... 267 12.1 The Population Regression Line 268 12.2 The Sample Regression Line 269 12.2.1 The Best Sample Line: Ordinary Least Squares 269 12.2.2 Finding the Intercept and Slope 270 12.2.3 Interpreting the Intercept and Slope 272 12.3 Evaluating the Sample Regression Line 272 12.3.1 The Sum of Squared Errors 272 12.3.2 The Mean Square Error and Standard Error of the Estimate 273 12.3.3 R2: The Coefficient of Determination 274 12.3.4 Testing the Sample Regression Line 275 12. 4 Evaluating the Sample Regression Slope 276 12.5 The Relationship of F and t: Here and Beyond 278 12.6 Predictions Using the Regression Line 278 12.6.1 Using the Regression Line to Predict Y Given X 278 12.6.2 Confidence Intervals for Y Given X 279 12.7 Regression and Correlation 281 12.7.1 Finding a Sample Correlation 281 12.7.2 Interpreting a Sample Correlation 282 12.7.3 Testing a Sample Correlation 282 12.7.4 The Relationship of Regression and Correlation 283 12.8 Another Example 283 12.9 Dummy Explanatory Variables 287 12.10 The Need for Multiple Regression 291 12.11 Exercises 292 13 Multiple Regression............................................................................................ 297 13.1 Extensions of Regression Analysis 297 13.1.1 When There Is More Than One Cause 297 13.1.2 When the Line Is Not Straight 297 13.2 The Population Regression Line 298 13.3 The Sample Regression Line 299 13.3.1 The Best Sample Line: Ordinary Least Squares 299 13.3.2 Finding the Intercept and Slopes: A Job for the Computer 300 13.3.3 Interpreting the Intercept and Slopes 300 13.4 Evaluating the Sample Regression Line 301 13.4.1 The Sum of Squared Errors 301 13.4.2 The Mean Square Error and Standard Error of the Estimate 301 13.4.3 R2 and R2: The Coefficients of Determination 301 13.4.4 Testing the Sample Regression Line 302 13.5 Evaluating the Sample Regression Slopes 303 13.6 Predictions Using the Regression Line 304 13.6.1 Using the Regression Line to Predict Y Given the X, 304 13.6.2 Confidence Intervals for Y Given the X, 304 13.7 Categorical Variables 306 13.8 Estimating Curved Lines 309 13.8.1 The Quadratic Function 309 13.8.2 The Cobb­Douglas (Log­Log) Function 313 13.9 Additional Examples 316 13.10 Exercises 326 14 Time-Series Analysis ......................................................................................... 329 14.1 Exploiting Patterns over Time 329 14.2 The Basic Components of a Time Series 330 14.3 Moving Averages 332 14.4 Seasonal Variation 333 14.4.1 Using a Moving Average to Create a Seasonal Index 334 14.4.1.1 Finding a Centered, Seasonally Balanced Moving Average 334 14.4.1.2 Finding Specific Seasonal Indexes 335 14.4.1.3 Finding an Overall Seasonal Index 335 14.4,2 Using a Seasonal Index 336 14.5 The Long-Term Trend 338 14.5.1 A Linear Trend 338 14.5.2 An Exponential (Semilog) Trend 340 14.5.3 The Limitations of Curve-Fitting 344 14.6 The Business Cycle 345 14.7 Putting It All Together: Forecasting 345 14.7.1 Recapping Our Decomposition 345 14.7.1.1 Seasonal Variation 346 14.7.1.2 Long-Term Trend 346 14.7.1.3 Cyclical and Random Variation 346 14.7.2 Projecting the Trend 346 14.7.3 Projecting the Business Cycle 346 14.7.4 Projecting Seasonal Variation 348 14.8 Another Example 349 14.9 Exercises 355 Appendix A .............................................................................................................. 359 Examples, Exercises, and Data Files 359 Appendix B: Answers to Odd-Numbered Exercises................................................. 365 Chapter 1: Introduction to Statistics 365 Chapter 2: Describing Data: Tables and Graphs 365 Chapter 3: Describing Data: Summary Statistics 379 Chapter 4: Basic Probability 383 Chapter 5: Probability Distributions 385 Chapter 6: Sampling and Sampling Distributions 387 Chapter 7: Estimation and Confidence Intervals 392 Chapter 8: Tests of Hypotheses: One-Sample Tests 396 Chapter 9: Tests of Hypotheses: Two-Sample Tests 400 Chapter 10: Tests of Hypotheses: Contingency and Goodness-of-Fit 413 Chapter 11: Tests of Hypotheses: ANOVA and Tests of Variances 421 Chapter 12: Simple Regression and Correlation 427 Chapter 13: Multiple Regression 435 Chapter 14: Time-Series Analysis 444 Appendix C .............................................................................................................. 449 Index........................................................................................................................ 467

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