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Describe a hypothesis test that you would like to conduct. Be sure to include the null and alternate hypotheses as well as the data you would need to collect to conduct the test. Discuss which level of significance you would use and why you would use that level. Further explain what you would do if you obtained a test statistic that was equal to the critical value.Week 1: Provide your initial discussion post to the question. Be sure to include references to any resources you used. You should use at least one resource to help you with your initial discussion. introductorybusinessstatistics_op_mxkhmqw__1_.pdf Unformatted Attachment Preview 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. 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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 Cohens 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 5 8 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 1 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. 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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: 2 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 ... Purchase answer to see full attachment