Step 1 :1. Test statistic: t = \(\frac{M_1 - M_2}{\sqrt{\frac{S_{1}^{2}}{n_1} + \frac{S_{2}^{2}}{n_2}}}\) = \(\frac{82.5 - 70}{\sqrt{\frac{15.3^2}{23} + \frac{20.2^2}{25}}}\) = 6.099
Step 2 :2. Degrees of freedom: \(\min(n_1 - 1, n_2 - 1)\) = \(\min(22, 24)\) = 22
Step 3 :3. p-value: p = 2 × P(T ≥ 6.099) with df = 22, using t-distribution table, p < 0.0001