Hypothesis Test for a Mean (t-Test)
One-sample t-test with σ unknown: test statistic, p-value, critical value, decision, conclusion.
Use when σ is unknown (estimated by s). Degrees of freedom = n − 1.
① Answer
② Steps
③ Why it works
When σ is unknown we estimate it with s — and that extra estimation adds uncertainty, so the sampling distribution gets heavier tails: Student’s t with n − 1 degrees of freedom. Everything else mirrors the z-test: t-statistic, p-value from the t curve, compare with α. As n grows the t curve melts into the normal curve.