Introductory business statistics op

You are probably asking yourself the question, When and where will I use statistics? If you read any newspaper, watch television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a television news program, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or fact. Statistical methods can help you make the best educated guess. Since you will undoubtedly be given statistical information at some point in your life, you need to know some techniques for analyzing the information thoughtfully. Think about buying a house or managing a budget. Think about your chosen profession. The fields of economics, business, psychology, education, biology, law, computer science, police science, and early childhood development require at least one course in statistics. Included in this chapter are the basic ideas and words of probability and statistics. You will soon understand that statistics and probability work together. You will also learn how data are gathered and what good data can be distinguished from bad.

Introductory Business Statistics SENIOR CONTRIBUTING AUTHORS ALEXANDER HOLMES, THE UNIVERSITY OF OKLAHOMA BARBARA ILLOWSKY, DE ANZA COLLEGE SUSAN DEAN, DE ANZA COLLEGE OpenStax Rice University 6100 Main Street MS-375 Houston, Texas 77005 To learn more about OpenStax, visit https://openstax.org Individual print copies and bulk orders can be purchased through our website ©2018 Rice University Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0) Under this license, any user of this textbook or the textbook contents herein must provide proper attribution as follows: - - - - If you redistribute this textbook in a digital format (including but not limited to PDF and HTML), then you must retain on every page the following attribution: “Download for free at https://openstax.org/details/books/introductory-business-statistics.” If you redistribute this textbook in a print format, then you must include on every physical page 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openstax.org/details/books/introductory-business-statistics Access The future of education openstax.org Table of Contents Preface Chapter 1: Sampling and Data 1.1 Definitions of Statistics, Probability, and Key Terms 1.2 Data, Sampling, and Variation in Data and Sampling 1.3 Levels of Measurement 1.4 Experimental Design and Ethics Chapter 2: Descriptive Statistics 2.1 Display Data 2.2 Measures of the Location of the Data 2.3 Measures of the Center of the Data 2.4 Sigma Notation and Calculating the Arithmetic Mean 2.5 Geometric Mean 2.6 Skewness and the Mean, Median, and Mode 2.7 Measures of the Spread of the Data Chapter 3: Probability Topics 3.1 Terminology 3.2 Independent and Mutually Exclusive Events 3.3 Two Basic Rules of Probability 3.4 Contingency Tables and Probability Trees 3.5 Venn Diagrams Chapter 4: Discrete Random Variables 4.1 Hypergeometric Distribution 4.2 Binomial Distribution 4.3 Geometric Distribution 4.4 Poisson Distribution Chapter 5: Continuous Random Variables 5.1 Properties of Continuous Probability Density Functions 5.2 The Uniform Distribution 5.3 The Exponential Distribution Chapter 6: The Normal Distribution 6.1 The Standard Normal Distribution 6.2 Using the Normal Distribution 6.3 Estimating the Binomial with the Normal Distribution Chapter 7: The Central Limit Theorem 7.1 The Central Limit Theorem for Sample Means 7.2 Using the Central Limit Theorem 7.3 The Central Limit Theorem for Proportions 7.4 Finite Population Correction Factor Chapter 8: Confidence Intervals 8.1 A Confidence Interval for a Population Standard Deviation, Known or Large Sample Size 8.2 A Confidence Interval for a Population Standard Deviation Unknown, Small Sample Case 8.3 A Confidence Interval for A Population Proportion 8.4 Calculating the Sample Size n: Continuous and Binary Random Variables Chapter 9: Hypothesis Testing with One Sample 9.1 Null and Alternative Hypotheses 9.2 Outcomes and the Type I and Type II Errors 9.3 Distribution Needed for Hypothesis Testing 9.4 Full Hypothesis Test Examples Chapter 10: Hypothesis Testing with Two Samples 10.1 Comparing Two Independent Population Means 10.2 Cohen's Standards for Small, Medium, and Large Effect Sizes 10.3 Test for Differences in Means: Assuming Equal Population Variances 10.4 Comparing Two Independent Population Proportions 10.5 Two Population Means with Known Standard Deviations 10.6 Matched or Paired Samples Chapter 11: The Chi-Square Distribution 11.1 Facts About the Chi-Square Distribution 5 21 29 45 46 64 71 75 76 77 79 133 133 138 146 151 163 203 205 206 209 214 241 242 246 249 279 280 282 289 307 308 310 318 320 333 334 343 346 350 381 382 383 386 392 419 420 427 428 429 432 435 465 466 11.2 Test of a Single Variance 11.3 Goodness-of-Fit Test 11.4 Test of Independence 11.5 Test for Homogeneity 11.6 Comparison of the Chi-Square Tests Chapter 12: F Distribution and One-Way ANOVA 12.1 Test of Two Variances 12.2 One-Way ANOVA 12.3 The F Distribution and the F-Ratio 12.4 Facts About the F Distribution Chapter 13: Linear Regression and Correlation 13.1 The Correlation Coefficient r 13.2 Testing the Significance of the Correlation Coefficient 13.3 Linear Equations 13.4 The Regression Equation 13.5 Interpretation of Regression Coefficients: Elasticity and Logarithmic Transformation 13.6 Predicting with a Regression Equation 13.7 How to Use Microsoft Excel® for Regression Analysis Appendix A: Statistical Tables Appendix B: Mathematical Phrases, Symbols, and Formulas Index This OpenStax book is available for free at http://cnx.org/content/col11776/1.33 466 470 477 482 485 513 513 517 517 526 551 552 555 556 558 571 574 577 595 613 621 Preface PREFACE Welcome to Introductory Business Statistics, an OpenStax resource This textbook was written to increase student access to high-quality learning materials, maintaining highest standards of academic rigor at little to no cost About OpenStax OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education Our first openly licensed college textbook was published in 2012, and our library has since scaled to over 25 books for college and AP® courses used by hundreds of thousands of students OpenStax Tutor, our low-cost personalized learning tool, is being used in college courses throughout the country Through our partnerships with philanthropic foundations and our alliance with other educational resource organizations, OpenStax is breaking down the most common barriers to learning and empowering students and instructors to succeed About OpenStax resources Customization Introductory Business Statistics is licensed under a Creative Commons Attribution 4.0 International (CC BY) license, which means that you can distribute, remix, and build upon the content, as long as you provide attribution to OpenStax and its content contributors Because our books are openly licensed, you are free to use the entire book or pick and choose the sections that are most relevant to the needs of your course Feel free to remix the content by assigning your students certain chapters and sections in your syllabus, in the order that you prefer You can even provide a direct link in your syllabus to the sections in the web view of your book Instructors also have the option of creating a customized version of their OpenStax book The custom version can be made available to students in low-cost print or digital form through their campus bookstore Visit the Instructor Resources section of your book page on OpenStax.org for more information Errata All OpenStax textbooks undergo a rigorous review process However, like any professional-grade textbook, errors sometimes occur Since our books are web based, we can make updates periodically when deemed pedagogically necessary If you have a correction to suggest, submit it through the link on your book page on OpenStax.org Subject matter experts review all errata suggestions OpenStax is committed to remaining transparent about all updates, so you will also find a list of past errata changes on your book page on OpenStax.org Format You can access this textbook for free in web view or PDF through OpenStax.org, and for a low cost in print About Introductory Business Statistics Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises The result is a meaningful understanding of the discipline which will serve students in their business careers and real-world experiences Coverage and scope Introductory Business Statistics began as a customized version of OpenStax Introductory Statistics by Barbara Illowsky and Susan Dean Statistics faculty at The University of Oklahoma have used the business statistics adaptation for several years, and the author has continually refined it based on student success and faculty feedback The book is structured in a similar manner to most traditional statistics textbooks The most significant topical changes occur in the latter chapters on regression analysis Discrete probability density functions have been reordered to provide a logical progression from simple counting formulas to more complex continuous distributions Many additional homework assignments have been added, as well as new, more mathematical examples Introductory Business Statistics places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data To achieve this unique approach, the author included a wealth of additional material and purposely de-emphasized the use of the scientific calculator Specific changes regarding formula use include: Preface • Expanded discussions of the combinatorial formulas, factorials, and sigma notation • Adjustments to explanations of the acceptance/rejection rule for hypothesis testing, as well as a focus on terminology regarding confidence intervals • Deep reliance on statistical tables for the process of finding probabilities (which would not be required if probabilities relied on scientific calculators) • Continual and emphasized links to the Central Limit Theorem throughout the book; Introductory Business Statistics consistently links each test statistic back to this fundamental theorem in inferential statistics Another fundamental focus of the book is the link between statistical inference and the scientific method Business and economics models are fundamentally grounded in assumed relationships of cause and effect They are developed to both test hypotheses and to predict from such models This comes from the belief that statistics is the gatekeeper that allows some theories to remain and others to be cast aside for a new perspective of the world around us This philosophical view is presented in detail throughout and informs the method of presenting the regression model, in particular The correlation and regression chapter includes confidence intervals for predictions, alternative mathematical forms to allow for testing categorical variables, and the presentation of the multiple regression model Pedagogical features • Examples are placed strategically throughout the text to show students the step-by-step process of interpreting and solving statistical problems To keep the text relevant for students, the examples are drawn from a broad spectrum of practical topics; these include examples about college life and learning, health and medicine, retail and business, and sports and entertainment • Practice, Homework, and Bringing It Together give the students problems at various degrees of difficulty while also including real-world scenarios to engage students Additional resources Student and instructor resources We’ve compiled additional resources for both students and instructors, including Getting Started Guides, an instructor solution manual, and PowerPoint slides Instructor resources require a verified instructor account, which you can apply for when you log in or create your account on OpenStax.org Take advantage of these resources to supplement your OpenStax book Community Hubs OpenStax partners with the Institute for the Study of Knowledge Management in Education (ISKME) to offer Community Hubs on OER Commons – a platform for instructors to share community-created resources that support OpenStax books, free of charge Through our Community Hubs, instructors can upload their own materials or download resources to use in their own courses, including additional ancillaries, teaching material, multimedia, and relevant course content We encourage instructors to join the hubs for the subjects most relevant to your teaching and research as an opportunity both to enrich your courses and to engage with other faculty To reach the Community Hubs, visit www.oercommons.org/hubs/OpenStax Technology partners As allies in making high-quality learning materials accessible, our technology partners offer optional low-cost tools that are integrated with OpenStax books To access the technology options for your text, visit your book page on OpenStax.org About the authors Senior contributing authors Alexander Holmes, The University of Oklahoma Barbara Illowsky, DeAnza College Susan Dean, DeAnza College Contributing authors Kevin Hadley, Analyst, Federal Reserve Bank of Kansas City Reviewers Birgit Aquilonius, West Valley College Charles Ashbacher, Upper Iowa University - Cedar Rapids Abraham Biggs, Broward Community College This OpenStax book is available for free at http://cnx.org/content/col11776/1.33 Appendix A 609 v 0.10 19 0.05 0.025 0.01 0.005 0.001 1.328 1.729 2.093 2.539 2.861 3.579 20 1.325 1.725 2.086 2.528 2.845 3.552 21 1.323 1.721 2.080 2.518 2.831 3.527 22 1.321 1.717 2.074 2.508 2.819 3.505 23 1.319 1.714 2.069 2.500 2.807 3.485 24 1.318 1.711 2.064 2.492 2.797 3.467 25 1.316 1.708 2.060 2.485 2.787 3.450 26 1.315 1.706* 2.056 2.479 2.779 3.435 27 1.314 1.703 2.052 2.473 2.771 3.421 28 1.313 1.701 2.048 2.467 2.763 3.408 29 1.311 1.699 2.045 2.462 2.756 3.396 30 1.310 1.697 2.042 2.457 2.750 3.385 40 1.303 1.684 2.021 2.423 2.704 3.307 60 1.296 1.671 2.000 2.390 2.660 3.232 100 1.290 1.660 1.984 2.364 2.626 3.174 ∞ 2.326 2.576 3.090 1.282 1.645 1.960 Table A12 Probability of Exceeding the Critical Value NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, September 2011 Figure A4 610 Appendix A χ2 Probability Distribution df 0.995 0.990 0.975 0.950 0.900 0.100 0.050 0.025 0.010 0.005 0.000 0.000 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860 0.412 0.554 0.831 1.145 1.610 9.236 11.070 12.833 15.086 16.750 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.548 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 20.278 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 21.955 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 23.589 10 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.188 11 2.603 3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 26.757 12 3.074 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 28.300 13 3.565 4.107 5.009 5.892 7.042 19.812 22.362 24.736 27.688 29.819 14 4.075 4.660 5.629 6.571 7.790 21.064 23.685 26.119 29.141 31.319 15 4.601 5.229 6.262 7.261 8.547 22.307 24.996 27.488 30.578 32.801 16 5.142 5.812 6.908 7.962 9.312 23.542 26.296 28.845 32.000 34.267 17 5.697 6.408 7.564 8.672 10.085 24.769 27.587 30.191 33.409 35.718 18 6.265 7.015 8.231 9.390 10.865 25.989 28.869 31.526 34.805 37.156 19 6.844 7.633 8.907 10.117 11.651 27.204 30.144 32.852 36.191 38.582 20 7.434 8.260 9.591 10.851 12.443 28.412 31.410 34.170 37.566 39.997 21 8.034 8.897 10.283 11.591 13.240 29.615 32.671 35.479 38.932 41.401 22 8.643 9.542 10.982 12.338 14.041 30.813 33.924 36.781 40.289 42.796 23 9.260 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 44.181 24 9.886 10.856 12.401 13.848 15.659 33.196 36.415 39.364 42.980 45.559 25 10.520 11.524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 46.928 26 11.160 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 48.290 27 11.808 12.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 49.645 28 12.461 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 50.993 29 13.121 14.256 16.047 17.708 19.768 39.087 42.557 45.722 49.588 52.336 30 13.787 14.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 53.672 40 20.707 22.164 24.433 26.509 29.051 51.805 55.758 59.342 63.691 66.766 50 27.991 29.707 32.357 34.764 37.689 63.167 67.505 71.420 76.154 79.490 60 35.534 37.485 40.482 43.188 46.459 74.397 79.082 83.298 88.379 91.952 70 43.275 45.442 48.758 51.739 55.329 85.527 90.531 95.023 100.425 104.215 Table A13 Area to the Right of the Critical Value of χ2 This OpenStax book is available for free at http://cnx.org/content/col11776/1.33 Appendix A 611 df 0.995 0.990 0.975 0.950 0.900 0.100 0.050 0.025 0.010 0.005 80 51.172 53.540 57.153 60.391 64.278 96.578 90 59.196 61.754 65.647 69.126 73.291 107.565 113.145 118.136 124.116 128.299 101.879 106.629 112.329 116.321 100 67.328 70.065 74.222 77.929 82.358 118.498 124.342 129.561 135.807 140.169 Table A13 Area to the Right of the Critical Value of χ2 612 This OpenStax book is available for free at http://cnx.org/content/col11776/1.33 Appendix A Appendix B 613 APPENDIX B: MATHEMATICAL PHRASES, SYMBOLS, AND FORMULAS English Phrases Written Mathematically When the English says: Interpret this as: X is at least X≥4 The minimum of X is X≥4 X is no less than X≥4 X is greater than or equal to X ≥ X is at most X≤4 The maximum of X is X≤4 X is no more than X≤4 X is less than or equal to X≤4 X does not exceed X≤4 X is greater than X>4 X is more than X>4 X exceeds X>4 X is less than X