When the two independent small samples of sizes $n_1$ and $n_2$ with means $\overline{x_1}$ and $\overline{x_2}$, respectively are drawn from populations with identical population variances, the test-statistic is computed as
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $t=\frac{\overline{x_1}-\overline{x_2}}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_1}}}$, where $S_p$, is pooled standard deviation.
For two independent small samples of sizes $n_1$ and $n_2$ drawn from populations with identical variances, the pooled standard deviation is used.
The test statistic is
$t=\frac{\bar x_1-\bar x_2}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$
where $S_p$ is the pooled standard deviation.