A test statistic is a single number computed from your sample that measures how far the sample result sits from what the null hypothesis predicts, expressed in units of standard error. Because every test statistic is compared against a reference distribution — the standard normal curve for a z-test, a t-distribution with a particular number of degrees of freedom for a t-test — you cannot interpret the number without knowing which sampling distribution it belongs to. The sampling distribution is what turns an abstract distance into a probability statement, and that probability is the p-value.
In this course the practical skills are: identify what is known and unknown about the population (is sigma given, or only the sample standard deviation s?), pick the matching test statistic, compute it correctly, determine the degrees of freedom when using t, and convert the result into a p-value you can compare against alpha. These steps sit at the heart of nearly every engineering hypothesis test you will run, from verifying a manufacturing tolerance to checking a vendor's performance claim.
As you watch, keep three questions in front of you: What is being subtracted from what in the numerator? What goes in the denominator, and why is it a standard error rather than a standard deviation? And which curve is the resulting value being compared against? If you can answer those for each example, the formulas stop being things to memorize and become things you can reconstruct.
Joshua Emmanuel works through a complete one-tailed hypothesis test about a fitness app's claim regarding average daily exercise time, in the case where the population standard deviation sigma is known. Based on the title and description, it should cover stating the hypotheses, computing the z-test statistic from the sample mean, and reaching a conclusion about the claim. This is the classic known-sigma scenario that defines when the z-test statistic is the right choice.
It gives a clean, fully worked z-test on a realistic claim, which directly supports the 'What Is a Test Statistic?' and 'The Z-Test Statistic' subtopics; Joshua Emmanuel's statistics tutorials are widely used and known for clear, step-by-step numerical work.
This Study Hall episode addresses probability distributions and, per its description, how sampling distributions and test statistics are used to judge what counts as typical versus unlikely given expectations. It should build the conceptual bridge between a distribution of possible sample outcomes and the decision rule used in a hypothesis test. Expect emphasis on reasoning and intuition rather than heavy computation.
It is the best fit for the 'Sampling Distributions and Their Role' and 'Connecting the Test Statistic to a P-Value' subtopics, and the Study Hall / Crash Course production style keeps the conceptual framing accessible before you dive into formulas.
A short, focused comparison of the z-test and the t-test aimed at helping you decide which one a given problem calls for. The video is organized around the selection criteria — typically whether the population standard deviation is known and how large the sample is — rather than around a single worked example.
It maps directly onto the 'Choosing the Right Test Statistic' subtopic and reinforces 'The t-Test Statistic' and 'Degrees of Freedom' by contrasting the t-distribution with the normal, which is exactly the decision students most often get wrong.
Together these videos build the computational core of the module. The Study Hall episode establishes why a sampling distribution is needed before any p-value can be interpreted, and the Joshua Emmanuel walkthrough demonstrates the full cycle of stating hypotheses, computing a test statistic, and converting it to a conclusion — supporting MO1, MO3, and MO4. The z-versus-t comparison trains the selection judgment required by MO2 and clarifies the role of degrees of freedom when sigma is unknown. None of the three focuses on Type I and Type II errors (MO5), so pair them with the module readings and lecture material on error types and on the broader test families (paired t, chi-square, ANOVA) referenced in MO2.
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.