Build the 90 % Welch interval for μ₁ − μ₂ from the billing-system data (difference 7.1, SE from s₁ = 9.5, n₁ = 12, s₂ = 6.8, n₂ = 10) using the given t(0.05; 9) = 1.833.

Answer

import math diff = 31.2 - 24.1 se = math.sqrt(9.5**2 / 12 + 6.8**2 / 10) t_crit = 1.833 lo, hi = diff - t_crit * se, diff + t_crit * se print(f"90% CI: {lo:.2f} to {hi:.2f}")

IBS1 §10.1, CC BY 4.0; H-W9 (90 % CI for the difference) — shape only; original dataset