In earlier parts of this module you learned the logic of hypothesis testing: stating a null and alternative hypothesis, choosing a significance level, computing a test statistic, and deciding whether the evidence is strong enough to reject the null. This topic turns that logic into practice. Engineering data arrives in many shapes — one sample compared to a specification, two independent production lines, before-and-after measurements on the same units, counts in categories, or three or more treatment groups — and each shape calls for a different test.
The practical skill is matching the data scenario to the right procedure. Ask yourself: Is the response measured on a continuous scale or is it a count in categories? How many groups are being compared? Are the observations in the two groups independent, or are they naturally paired? Answering those questions leads you to the one-sample t-test, the two-sample t-test, the paired t-test, a chi-square test, or ANOVA. Getting this choice wrong invalidates everything that follows, no matter how carefully you compute the arithmetic.
The videos below focus on two of the trickier cases: paired data and categorical count data. While watching, pay attention to how each hypothesis is worded, where the degrees of freedom come from, how the test statistic is assembled from the sample values, and — most importantly — how the final numerical result is translated back into a plain-language conclusion about the original question. Try pausing before the solution is revealed and working the example yourself.
This tutorial works through a two-tailed paired (repeated measures) t-test starting from raw data, so you can see how the paired differences are formed before any test statistic is computed. The description indicates it also covers the related matched-subjects setup and the construction of a confidence interval alongside the test. Expect to see the hypotheses stated, the test statistic calculated, and a conclusion drawn.
It directly supports the Paired t-Test for Before-and-After Data subtopic and clarifies the distinction between paired and independent designs — exactly the judgment call needed when selecting the right test. Joshua Emmanuel's channel is widely used in engineering statistics courses for compact, worked numerical examples.
This video explains the chi-square goodness-of-fit test using a single worked example, showing how observed category counts are compared against expected counts under the null hypothesis. You should see how expected frequencies are generated, how the chi-square statistic accumulates contributions across categories, and how degrees of freedom are determined before the decision is made.
It covers the Chi-Square Test for Categorical Data subtopic for the single-variable case, and reinforces that categorical count data requires a different sampling distribution than the t-tests used for continuous measurements.
This video introduces the chi-square test of independence using a contingency table, where two categorical variables are cross-classified. It is a brief, example-driven explanation that walks through setting up the table, obtaining expected counts from row and column totals, and testing whether the two variables are associated.
It completes the chi-square portion of this topic by addressing the two-variable case, and it pairs naturally with the goodness-of-fit video so you can tell the two chi-square procedures apart when choosing a test for real data.
Together these videos give you repeated practice with the core steps the module outcomes demand. Each one begins by stating null and alternative hypotheses from a concrete scenario (MO1) and then carries the example through to a test statistic, degrees of freedom, and a p-value or critical-value comparison (MO3), ending with an explicit accept/reject decision at a stated significance level (MO4). Because the three videos cover three distinct situations — paired continuous measurements, a single categorical variable, and two cross-classified categorical variables — they build the pattern recognition needed to choose correctly among the paired t-test, chi-square, and the other tests in your toolkit (MO2). As you watch, consider what a wrong rejection or a missed effect would mean in an engineering setting, and supplement these examples with the course material on one-sample tests, two-sample tests, ANOVA, and Type I versus Type II error (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.