For H₀: μ = 200 vs Hₐ: μ ≠ 200 with n = 10, x̄ = 212.4, s = 18.6 and the given t(0.025; 9) = 2.262, compute t, decide, and check that 200 lies inside the 95 % interval (199.10, 225.70).

Answer

import math n, xbar, s, mu0, t_crit = 10, 212.4, 18.6, 200, 2.262 se = s / math.sqrt(n) t = (xbar - mu0) / se decision = "reject" if abs(t) > t_crit else "do not reject" print(f"t={t:.3f} critical={t_crit} decision={decision}") lo, hi = xbar - t_crit * se, xbar + t_crit * se print(f"{mu0} inside ({lo:.2f}, {hi:.2f}): {lo < mu0 < hi}")

BCc ch 3; H-W7 (part b, "a test of sorts") — shape only; original dataset