Mistake Master
An Interval of Gaps, Not of Scores
You'll learnhow the two-sample t interval is assembled from its three pieces, why the critical value comes from the t family and what the z habit silently costs, which conditions run once and which run twice, what the four-part interpretation must contain, and what actually narrows an interval.
Method A scored 78.4 from 30 students; method B scored 71.2 from 28. The difference is 7.2 points — and 7.2 from one pair of samples is not the answer, it is the center of one. Reach t* standard errors both ways: 7.2 ± 2.052 × 2.341 = 7.2 ± 4.80, giving (2.40, 12.00). Every number in that range is a plausible GAP between the two population means — not a score — and zero is not among them, which is what lets the study say method A is plausibly ahead. Use z's 1.96 instead of t's 2.052 and the interval claims 95 percent while covering about 94: this page integrates the t distribution and prints the shortfall, rather than asking you to take the t table on faith. Twelve short steps; press Next for each one.