In Week 9 you tested claims about a single population parameter. Engineering questions, though, are usually comparative: Does the new alloy last longer than the old one? Does supplier B's bearing diameter differ from supplier A's? Two-sample hypothesis tests answer these questions by asking whether an observed difference between two sample means is large enough to be inconsistent with the hypothesis that the two populations have the same mean.
The logic is the same as before, but the sampling distribution now describes a difference of means. The null hypothesis is typically that the difference is zero, the standard error combines variability from both groups, and the test statistic measures how many standard errors the observed difference sits from the hypothesized value. Which statistic you use depends on what you know: if both population standard deviations are known (or samples are large), a two-sample z-test applies; if the standard deviations are estimated from the data, a two-sample t-test with an appropriate degrees-of-freedom rule applies. Underlying both is the assumption that the two samples are independent of each other and drawn randomly, with approximate normality or large enough samples for the Central Limit Theorem to help.
As you watch the videos below, track four things in every worked example: how the hypotheses are written in terms of the difference of means, how the standard error is built from the two sample sizes, where the degrees of freedom come from in the t-test, and how the final p-value or critical-value comparison is translated into a conclusion stated in the language of the original problem. Pay particular attention to the moment each presenter decides whether the samples are independent, because that single judgment determines whether this module's methods apply at all.
A full worked example of a hypothesis test comparing two population means when both population standard deviations are known and the samples are independent. Over its longer runtime it should walk through hypothesis setup, the standard error for a difference of means, computation of the z statistic, and the decision rule.
The extended length allows the complete procedure to be shown step by step rather than summarized, which makes it a good first exposure to the two-sample z-test and the independence condition it requires.
A lecture segment from the University of Illinois Data Science Discovery course covering the two-sample z-test. As part of a structured university course sequence, it should present the test in the context of comparing two groups and interpreting the resulting evidence.
It offers a second, university-produced treatment of the same test, which is useful for seeing the logic framed in a different notation and applied in a data-analysis setting.
A compact how-to on carrying out a two-sample t-test for a difference in means, aimed at students learning significance testing. Expect the conditions to be checked, the t statistic computed from sample standard deviations, and the p-value used to reach a conclusion.
This is the direct companion to the z-test videos for the far more common case where population standard deviations are unknown, and its short format makes it easy to review before problem sets.
Together these videos build the core skills of the module. The z-test and t-test examples let you contrast when each statistic is appropriate based on what is known about the population standard deviations and on sample independence (MO1), and each demonstrates the standard error, test statistic, and degrees-of-freedom mechanics you will reproduce by hand (MO2). The explicit condition checks in the t-test video reinforce how to verify randomness, independence, and approximate normality before trusting a result (MO3), while the concluding steps in all three model how to move from a p-value to a decision stated in context (MO4). The videos do not address non-parametric alternatives, so plan to rely on the course notes and lecture for MO5.
These videos were chosen from YouTube on October 2, 2026. Each has captions; the player turns them on. Videos on YouTube can be changed or removed — if one no longer plays, tell your instructor. If a player does not appear, use its Watch on YouTube link.