Many engineering questions come down to comparing two success rates: the defect rate from two production lines, the pass rate of two inspection methods, or the proportion of users who complete a task with two different interface designs. The two-proportion z-test gives you a formal way to decide whether an observed difference between two sample proportions is large enough to be considered real, or whether it is within the range you would expect from sampling variability alone.
The mechanics follow the same five-step logic you used for means, with a few specifics. You state hypotheses about p1 - p2 (usually H0: p1 = p2 against a one- or two-sided alternative), check that the samples are independent and random and that each group has enough expected successes and failures for the normal approximation to hold, pool the two samples into a single estimate of the common proportion under H0, form the z statistic by dividing the observed difference by its standard error, and convert z into a p-value for a decision in context.
As you watch, pay close attention to two things that students most often get wrong. First, why the pooled proportion is used in the test statistic (because H0 assumes the two proportions are equal) even though the unpooled standard error is used for a confidence interval. Second, how the tail area is computed: one-tailed versus two-tailed p-values, and how to read them from a z table or software. Try pausing each example before the arithmetic and working it yourself.
A focused walkthrough of the two-sample proportion hypothesis test, from stating the null and alternative hypotheses through computing and interpreting the result. Based on its title and series description, it sits within a broader hypothesis-testing sequence that covers null and alternative hypotheses and Type I/II errors, so the vocabulary and logic are set up before the formula appears.
It is the most directly on-topic video of the three, covering hypothesis setup, the test statistic, and the conclusion in one short pass, which matches the subtopic sequence for this lesson.
Joshua Emmanuel works through significance tests for a single population proportion, demonstrating both one-tailed and two-tailed cases and obtaining p-values using a z table. The examples show how the tail area is found and compared against a significance level to reach a decision.
It builds the proportion-testing foundation and, more importantly, drills the p-value step with a z table, which is exactly the skill you reuse unchanged in the two-proportion test; Joshua Emmanuel's statistics tutorials are widely used and carefully worked.
This video demonstrates how to carry out a two-sample z-test for proportions and, in addition, how to construct a confidence interval for the difference between the two proportions. Expect a worked example that moves from the sample counts through the test statistic to a conclusion, with the interval presented alongside.
Pairing the test with the confidence interval reinforces the connection between the two forms of inference and gives you a second, independent presentation of the same calculation to compare against the other videos.
Together these videos target the proportion half of this module. The two-sample videos support MO4 directly by showing how the pooled estimate feeds into the z statistic for p1 - p2, and they reinforce MO2 by reminding you to check independence and the success/failure counts before applying the normal approximation. The single-proportion video strengthens the p-value machinery that MO5 depends on, while the confidence-interval segment in the third video models the interval-plus-test interpretation MO5 asks for. MO1 and MO3 are covered elsewhere in the module, but recognizing that these tests assume two independent groups is a useful contrast to the paired designs discussed there.
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.