Week 10/Module 9 - Hypothesis Testing II

This reading introduces two-sample hypothesis tests, explaining how to compare means or other statistics from two independent populations to determine whether observed differences are statistically significant, and serves as a foundational reference for learners setting up and interpreting such tests.

This reading explains paired sample designs, where each observation in one group is linked to a corresponding observation in the other, covering how the pairing structure changes the appropriate statistical method and how learners should apply paired tests rather than independent-samples tests in these situations.

This reading provides a structured decision-making framework for choosing the correct statistical test based on study design, data type, sample size, and other conditions, helping learners and instructors systematically avoid common errors in test selection.

This reading details the underlying assumptions required for inferential tests to produce valid probability statements—such as normality, independence, and equal variances—and guides learners on how to check these conditions before drawing conclusions from their analyses.

This reading introduces non-parametric statistical methods as alternatives to parametric tests when standard assumptions like normality cannot be met, explaining the rationale for and basic application of these techniques for learners working with real-world data that violates parametric requirements.

This reading explains how to correctly interpret and communicate the outputs of hypothesis tests—including test statistics, p-values, degrees of freedom, and confidence intervals—helping learners avoid common misinterpretations and report results accurately in engineering contexts.

A lesson page introducing two-sample hypothesis tests for comparing means from two independent groups, covering the two-sample z-test and pooled versus unpooled t-tests with engineering examples such as comparing alloys or suppliers, which learners read to set up and compute comparative tests.

A lesson page on paired or matched-design experiments where the same specimen, machine, or site is measured twice, explaining why such data require the paired-sample t-test on differences rather than an independent-samples analysis.

A decision-framework lesson that helps learners choose among the two-sample z-test, pooled and unpooled t-tests, and the paired t-test by working through questions about data structure, sample size, and known variance.

A lesson page reviewing the assumptions behind each hypothesis test — independence, normality or sufficient sample size, and variance conditions — and explaining how to check them and what happens to p-values when they are violated.

An introductory lesson on non-parametric alternatives for data that violate normality or involve small, skewed, or contaminated samples, showing when rank-based methods are preferable to mean-based parametric tests.

A lesson on interpreting and reporting results, tracing the reasoning from test statistic to p-value to decision at a given significance level, and on communicating conclusions clearly in engineering reports and design reviews.

The consolidated module page compiling all six Week 10 topics — two-sample tests, paired comparisons, test selection, assumptions, non-parametric methods, and result interpretation — for reading or review in a single document.

A navigation page linking learners to the Module 9 PowerPoint slides, lecture video, and Google Colab notebook for hypothesis testing with single samples.

A comprehensive reading covering single-sample hypothesis testing concepts including null and alternative hypotheses, test selection, and related procedures, used by learners as the primary reference text for the module.

A graded discussion assignment requiring learners to query an AI about statistical methods relevant to Six Sigma Black Belt certification and then reflect on the feasibility and professional implications of pursuing that credential.