Week 11/Module 10 - 2 Sample Hypothesis Testing

This reading introduces the conceptual framework of two-sample hypothesis testing, explaining why comparative questions arise in engineering and science and how two-sample tests extend single-sample inference; learners use it to build foundational understanding before selecting and applying specific tests.

This reading explains the critical distinction between independent and paired samples, covering how each design is structured, how pairing affects variability and test selection, and when to use each approach; learners and instructors use it to ensure the correct test type is chosen before any analysis begins.

This reading outlines the statistical assumptions underlying pooled two-sample t-tests, Welch's t-test, and non-parametric alternatives such as the Mann-Whitney U test, explaining how to check each condition and what violations mean for test validity; learners use it as a pre-analysis checklist before running two-sample tests.

This reading covers the procedures for comparing two population means using pooled and Welch's t-tests, including hypothesis formulation, test-statistic calculation, p-value interpretation, and confidence intervals for the difference in means; learners use it as a step-by-step procedural guide for mean-comparison problems.

This reading explains the two-proportion z-test, covering how to set up hypotheses, calculate the pooled proportion and test statistic, interpret p-values, and construct confidence intervals for the difference between two population proportions; learners use it to analyze comparative rate or proportion problems.

This reading focuses on translating hypothesis test outputs—p-values, test statistics, and confidence intervals—into clear, context-specific conclusions and data-driven decisions; learners use it to practice communicating statistical results meaningfully rather than stopping at numerical output.

A foundational reading that extends one-sample inference to comparative engineering questions, introducing the logic of testing differences between two means, proportions, or variances and the hypothesis structures used to frame such comparisons.

A lesson distinguishing independent samples from paired (matched) designs, showing learners how study design determines which two-sample procedure and formula to apply before any calculation is attempted.

A reading on the assumptions underlying two-sample tests — random sampling, independence within and between groups, normality or sufficient sample size, and equal-variance considerations — so learners can verify conditions before trusting a p-value or confidence interval.

A core lesson on comparing two population means, covering the pooled and Welch t-tests, paired t-tests, test statistics, and confidence intervals for the difference in means with engineering examples such as alloy strength and cycle time.

A lesson on the two-proportion z-test, including the pooled proportion, test statistic, and confidence interval for the difference between two success rates such as defect or pass rates from competing processes.

A reading on translating test statistics, p-values, and confidence intervals into practical engineering and business decisions, including statistical versus practical significance and the limits of what the evidence supports.

The consolidated module page compiling all Week 11 readings on two-sample hypothesis testing into a single continuous document for review or printing.

A landing page that organizes and links to the module's core instructional resources — the PowerPoint slides, lecture video, and Google Colab notebook — for learners to access all materials in one place.

A detailed study reference explaining key two-sample hypothesis testing methods, including the independent samples t-test, paired t-test, and tests for two proportions, with definitions, characteristics, and supporting lecture links for learners to review concepts.

A graded discussion assignment asking learners to describe Design of Experiments within Six Sigma methodology and apply it to a real-world personal or professional scenario, prompting reflection and peer engagement.