Let two independent random samples of sizes \(n_1\) and \(n_2\) respectively have been drawn from the same normal population. Let \(\overline{X_1}\) and \(\overline{X_2}\) be the means and let \(s_1\) and \(s_2\) be their standard deviations. In order to test whether the the two sample means \(\overline{X_1}\) and \(\overline{X_2}\) differ significantly or not, the \(t\)-test statistic is given by

1. A \(t=\frac{\overline{X_1}-\overline{X_2}}{S / \sqrt{\frac{1}{n_1}-\frac{1}{n_2}}}, \quad S=\sqrt{\frac{n_1 s_1^2+n_2 s_2^2}{n_1+n_2-2}}\)
2. B \(t=\frac{\overline{X_1}-\overline{X_2}}{S / \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}, S=\sqrt{\frac{n_1 s_1^2+n_2 s_2^2}{n_1+n_2-2}}\)
3. C \(t=\frac{\overline{X_1}-\overline{X_2}}{s \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}, \quad S=\sqrt{\frac{n_1 s_1^2+n_2 s_2^2}{n_1+n_2-2}}\)
4. D \(t=\frac{\overline{X_1}+\overline{X_2}}{s \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}, \quad S=\sqrt{\frac{n_1 s_1^2+n_2 s_2^2}{n_1+n_2-2}}\)