Statistical Inference - A Short Course

Statistical Inference: A Short Course is general in nature and is appropriate for undergraduates and first-year graduates majoring in the natural sciences, the social sciences, or in business. The book offers sufficient material for a one-semester course without overwhelming students with "too fast a pace" or "too many" topics. The essential topics appear in the main body of the chapters and additional interesting topics can be found in the chapter appendices and chapter exercises. While Chapters 1-10 are fundamental to any basic statistics course, instructors can tailor their course and choose additional topical coverage from Chapters 11-13. This latter set of chapters is optional, and the topics therein can be selected with an eye towards student interests and needs. While most beginning statistics books discuss the concepts of simple random sampling and normality, this book takes such discussions a bit further. Specifically, key assumptions typically made in the areas of estimation and testing are a "random sample" of observations drawn from a "normal population." However, given a particular data set, how can it be determined that it actually constitutes a random sample and, secondly, how can it be concluded if the parent population can be taken to be normal? That is, can we proceed "as if" the sample is random? And can we operate "as if" the population is normal? Answers to these questions are provided by formal test procedures for randomness and for the assessment of normality. Other unique topics found in the book include determining a confidence interval for a population median, ratio estimation (a technique akin to estimating a population proportion), general discussions of randomness and causality, and nonparametric methods that serve as an alternative to parametric routines when the latter are not strictly applicable.A concise, easily accessible introduction to descriptive and inferential techniques§Statistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures.§The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality. To ensure a thorough understanding of all key concepts, Statistical Inference provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including:§How do we determine that a given dataset is actually a random sample?§With what level of precision and reliability can a population sample be estimated?§How are probabilities determined and are they the same thing as odds?§How can we predict the level of one variable from that of another?§What is the strength of the relationship between two variables?§The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material.§Statistical Inference: A Short Course is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.