Week 9 / Module 8 — Hypothesis Testing

A structured outline of the module's core topics covering hypothesis testing foundations, null and alternative hypothesis formulation, test statistics, sampling distributions, and p-values, used as a navigation guide for the module's content.

A landing page that organizes and links to the module's main learning resources — the PowerPoint slides, lecture video, and Google Colab notebook — giving learners a single access point for all Module 8 instructional materials.

A reading that explains the core concepts of hypothesis testing, including null and alternative hypotheses, test statistics, p-values, significance levels, and decision rules, serving as the primary reference text learners study before or alongside lectures.

A reading that introduces hypothesis testing as a framework for using sample data to make decisions about populations, covering core concepts such as the logic of statistical inference, burden of proof, and the structured steps of a hypothesis test — intended as foundational background for learners beginning the topic.

A reading that explains how to correctly formulate null and alternative hypotheses before collecting data, covering the roles of each hypothesis, directional versus non-directional tests, and common pitfalls in hypothesis specification — used by learners to practice translating research questions into formal statistical claims.

A reading that explains what a test statistic is, how it compresses sample data into a single value, and how sampling distributions (such as z, t, and chi-square) are used to evaluate that value under the null hypothesis — used by learners to understand the mathematical bridge between raw data and a hypothesis test decision.

A reading that explains p-values and significance levels (α), how they interact to form a decision rule for rejecting or failing to reject the null hypothesis, and how to correctly interpret p-values — used by learners to understand and apply the core decision-making mechanism of hypothesis testing.

A reading that walks through the step-by-step application of the most commonly used hypothesis tests — including one-sample z and t tests, two-sample tests, and chi-square tests — providing worked examples so learners can see how to select and execute the appropriate test for a given engineering or research scenario.

A reading that defines Type I errors (false positives) and Type II errors (false negatives), explains their relationship to α and statistical power, and discusses the consequences of each error type — used by learners to understand the trade-offs and risks inherent in any hypothesis testing decision.

A reading that addresses how to accurately interpret hypothesis test results and communicate findings without overstating conclusions, covering common misinterpretations of p-values, the distinction between statistical and practical significance, and best practices for reporting results — used by learners and instructors to ensure correct understanding and professional communication of statistical analyses.

A 45-question quiz bank containing applied hypothesis testing problems set in engineering contexts (e.g., ball bearings, concrete strength), used by instructors to assess learners' ability to formulate hypotheses and select appropriate tests.

A graded discussion assignment in which learners query an AI tool about statistical methodology for determining whether manufactured products meet specified tolerances, then post the prompt, AI response, and their own critical comments for peer discussion.

A group assignment that uses a provided sample problem to explore how sample size affects the accept/reject region at a given significance level, requiring teams to run multiple hypothesis tests and analyze the relationship between sample size and decision boundaries.