Interpret and construct intervals

A confidence interval has form estimate ± critical multiplier×SE. The margin of error is the multiplier times SE; width is twice that margin. For a normal population with known σ, mean CI is mean±z(1-α/2)σ/√n. With unknown σ, use mean±t(1-α/2,n-1)s/√n under the t-model assumptions. Higher confidence requires a wider interval for the same data. Frequentist confidence refers to long-run coverage of the procedure.