The balance between theory and applications offers mathematical support to enhance coverage when necessary, giving engineers and scientists the proper mathematical context for statistical tools and methods. Case studies provide deeper insight into the practicality of the concepts. Calculus is confined to elementary probability theory and probability distributions (Chapters1–3). Linear algebra and the use of matrices are applied only in Section 7.11, where treatment of multiple linear regression and analysis of variance is covered. Compelling exercise sets challenge students to use the concepts to solve problems that occur in many real-life scientific and engineering situations. Many exercises contain real data from studies in the fields of biomedical, bioengineering, business, computing, etc. Real-life applications of the Poisson, binomial, and hypergeometric distributions generate student interest using topics such as flaws in manufactured copper wire, highway potholes, hospital patient traffic, airport luggage screening, and homeland security. Class projects provide the opportunity for students to gather their own experimental data and draw inferences from that data. These projects illustrate the meaning of a concept or provide empirical understanding of important statistical results, and are suitable for either group or individual work. Statistical software coverage in the following case studies includes SAS® and MINITAB®, with screenshots and graphics as appropriate: Two-sample hypothesis testing Multiple linear regression Analysis of variance Use of two-level factorial-experiments Interaction plots provide examples of scientific interpretations and new exercises using graphics. End-of-chapter material strengthens the connections between chapters. “Pot Holes” comments remind students of the bigger picture and how each chapter fits into that picture. These notes also discuss limitations of specific procedures and help students avoid common pitfalls in misusing statistics. Topic outline Chapter 1: elementary overview of statistical inference and basic probability Chapter 2: random variables, probability distributions, and expectations Chapter 3: specific discrete and continuous distributions with illustrations of their use and relationships among them Chapter 4: materials on graphical methods; an important introduction to the notion of sampling distribution Chapters 5–6: one- and two- sample point and interval estimation, statistical hypothesis testing Chapters 7–9: simple and multiple linear regressions; analysis of variance; multi-factorial experiments