A hypothesis test ends with a number — the p-value — and a decision rule built around a threshold you choose before you look at the data. The p-value answers a narrow but useful question: if the null hypothesis were true, how likely is it that we would see a sample result at least as extreme as the one we actually got? The significance level, alpha, is the amount of risk you are willing to accept of rejecting a true null hypothesis. Comparing the two gives you a defensible, repeatable decision rule: reject the null when p is less than or equal to alpha, otherwise fail to reject it.
This matters in engineering because conclusions about material strength, process yield, calibration drift, or supplier quality are rarely obvious from the raw numbers. A p-value lets you state how much evidence your data provides against a claim, and alpha forces you to decide in advance how strong that evidence must be rather than rationalizing after the fact. Equally important is knowing what a p-value is not: it is not the probability the null hypothesis is true, not the probability your result happened by chance, and not a measure of how large or important an effect is.
As you watch, pay attention to three things. First, the exact wording used to define the p-value — the conditional phrasing "assuming the null is true" does a lot of work. Second, how one-tailed and two-tailed situations change the tail area being computed. Third, how each presenter translates the final comparison back into a sentence about the original claim, since on exams and in practice you will be graded on the interpretation as much as the arithmetic.
A compact, worked walkthrough of testing a claim about a population mean using the p-value approach when the population standard deviation is known. Based on its title and description, it covers computing the z test statistic, finding the corresponding tail probability from a z-table, and comparing that p-value to the significance level to reach a conclusion. Expect fully worked numerical examples rather than extended conceptual discussion.
This is the mechanical side of the topic done cleanly and quickly: it shows exactly how a p-value is produced from a test statistic and then compared to alpha, which is the core computational skill for this week.
A longer, friendly conceptual introduction to hypothesis testing built around the question "what is a p-value?" Created for the Summer of Math Exposition, it is aimed at building intuition for what the p-value measures and why the logic of testing works the way it does, with Part 2 continuing the discussion. Expect visual explanation and careful definitions rather than table lookups.
It directly addresses the conceptual subtopics — what a p-value is and how to interpret it in context — and the extended run time allows the kind of careful definition work that prevents the common misinterpretations.
Part of the AMBOSS medical statistics series, this video explains how p-values are reported and understood in published studies, including what statistical significance claims actually mean. It is framed around interpreting results rather than deriving them, so expect emphasis on reading a reported p-value correctly and on the limits of what significance tells you.
The applied-publication framing is an excellent complement to the computational videos, targeting interpretation in context and the misinterpretations that arise when a significance threshold is treated as proof.
Together these videos reinforce MO3 and MO4 most directly: the Joshua Emmanuel example shows how to compute a test statistic and convert it into a p-value using the correct sampling distribution, while all three videos model the comparison of that p-value to a pre-specified alpha and the distinction between a significant result and an important one. The Max Dudek introduction supports MO1 by situating the p-value within a properly stated null and alternative hypothesis and by clarifying how directional claims affect the tail area used. The AMBOSS video strengthens interpretation and connects to MO5, since understanding what alpha controls is the same as understanding the Type I error rate you have accepted. Use the shorter videos for procedure and the longer ones for the reasoning you will need to justify conclusions in writing.
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.