Build two t-intervals with the critical values given: 90 % from x̄ = 4.85, s = 1.10, n = 20 (t = 1.729) and 95 % from x̄ = 212.4, s = 18.6, n = 10 (t = 2.262). Print each as "lower to upper" to two decimals.

Answer

import math cases = [("90%", 4.85, 1.10, 20, 1.729), ("95%", 212.4, 18.6, 10, 2.262)] for level, xbar, s, n, t in cases: se = s / math.sqrt(n) margin = t * se print(f"{level}: {xbar - margin:.2f} to {xbar + margin:.2f}")

IBS1 §8.2 (the t-interval), CC BY 4.0; BCc ch 3; H-W7 (t-CI at 90 %; "how would it change if σ were known"; robustness guideline) — shape only; original dataset