Mistake Master
The p-Value Is Where the Interval Touches Zero
You'll learnhow the two-sample t statistic is assembled, how to read its p-value at either accepted df, what a conclusion must contain to be checkable, why pooling has no license here even when it barely changes the answer, and exactly how the test and the interval are the same statement.
One subtraction over one standard error: t = 7.2 / 2.341 = 3.08, and at the conservative 27 degrees of freedom the one-sided p-value is 0.0024. Then the part usually taught as a rule to memorise. The test and the interval do not merely "agree" — build the interval at confidence 1 − p and its critical value is the t whose tail area is p, which is 3.08 itself, so the half-width is 3.08 × 2.341 = 7.2 and the interval is exactly (0.00, 14.40). The p-value is the confidence level at which the lower endpoint lands on zero, and this page asserts it to the last bit rather than asking you to take it on faith. Twelve short steps; press Next for each one.