Every hypothesis test ends with a decision — reject the null hypothesis or fail to reject it — and that decision can be wrong in two distinct ways. A Type I error (a false positive) happens when we reject a null hypothesis that is actually true; its probability is the significance level, alpha, that we choose before collecting data. A Type II error (a false negative) happens when we fail to reject a null hypothesis that is actually false; its probability is called beta, and the complement, 1 minus beta, is the power of the test.
This matters in engineering because the two errors usually carry very different costs. Falsely concluding that a new alloy is stronger, that a process change reduced defects, or that a contaminant level exceeds a limit leads to one kind of expensive mistake; failing to detect a real problem leads to another. Choosing alpha, sample size, and effect size is therefore an engineering judgment about which error you can least afford, not just a statistical formality.
As you watch, keep track of four things: the 2-by-2 table of truth versus decision, which error alpha controls and which beta controls, why lowering alpha tends to raise beta when sample size is fixed, and how increasing sample size (or effect size) raises power without that trade-off. Also notice the careful wording used for conclusions — we never "accept" the null hypothesis, we only fail to reject it.
A short introduction that lays out the four possible outcomes of a hypothesis test: correctly rejecting, correctly failing to reject, and the two error types. Expect the standard decision-versus-reality table along with definitions of Type I and Type II errors and the probabilities attached to each.
Mathispower4u is a well-established source of concise, correct math explanations, and this video gives the foundational framework and vocabulary you need before discussing trade-offs or power.
An engineering-oriented treatment of Type I and Type II errors from LearnChemE, likely connecting the definitions to the sampling distributions under the null and alternative hypotheses. Expect discussion of how alpha is set by the analyst and how beta depends on the true parameter value, sample size, and variability.
Produced by chemical engineering faculty at CU Boulder, it frames the errors in a technical, applied context that matches how you will encounter false positives and false negatives in engineering decisions.
This video focuses on the power of a test, 1 minus beta, and how it relates directly to the chance of a Type II error. It is presented as a companion to a worked Type II error example, so expect the geometry of overlapping distributions and the factors that increase power.
Power is the key concept for minimizing Type II errors, and this video closes the loop on the alpha-beta trade-off that the first two videos set up.
These three videos target MO5 most directly: the first establishes the four-outcome framework and precise definitions of Type I and Type II errors, the second reinforces those definitions in an engineering setting where consequences differ, and the third explains power as the tool for controlling false negatives. Together they also support MO4, since understanding what alpha actually buys you clarifies what it means to compare a p-value to a significance level and why statistical significance is not the same as a practically important or risk-free conclusion. Pair them with your own course examples so you can state, in words, what each error would mean for a specific engineering claim.
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.