Week 9/Module 8 - Hypothesis Testing

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 conceptual reading that introduces hypothesis testing as a formal decision procedure, reframing engineering questions as "how surprising would this data be if the status quo were true?" and setting up the vocabulary used throughout the week.

A lesson on translating engineering claims into competing statements about a population parameter, explaining why the null hypothesis always carries the equality and how to choose one- versus two-sided alternatives before any calculation begins.

A reading that defines the test statistic as a standardized measure of distance between the sample result and the null-predicted value, and shows which reference sampling distribution (standard normal, t with given degrees of freedom, etc.) applies to each situation.

A lesson explaining the p-value as the probability of a result at least as extreme as the observed one when the null is true, and how to compare it to a pre-chosen significance level alpha to reach a reject / fail-to-reject decision.

A worked application page that puts the testing procedure into practice across common engineering data situations — one-sample, two-sample, and related comparisons — so learners can match a data scenario to the correct test and carry it through.

A reading contrasting Type I (false positive, probability alpha) and Type II (false negative, probability beta) errors, used to help learners reason about the trade-off between the two and its connection to power and sample size.

A closing lesson on correctly interpreting and writing up results, emphasizing what a p-value is not (e.g., the probability the null is true) and how to communicate conclusions in engineering reports, design reviews, and regulatory submissions.

A single compiled page containing all of the module's topic readings end to end, useful as a consolidated review document or printable version of the full Week 9 hypothesis testing module.

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 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.

An interactive browser-based lab that visualizes the standard normal curve, critical values (e.g., z = 1.645), rejection regions, and test statistics so learners can work through the 'burden of proof' logic of hypothesis testing hands-on and see how test statistics compare against critical thresholds.