Let two independent random samples of… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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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

Official previous-year question

Held on 15 May 2025 · Verified 13 Jul 2026.

Options

A
$t = \frac{\overline{X_1} - \overline{X_2}}{S / \sqrt{\frac{1}{n_1} - \frac{1}{n_2}}}$ , $S = \sqrt{\frac{n_1 s_1^2 + n_2 s_2^2}{n_1 + n_2 - 2}}$
B
$t = \frac{\overline{X_1} - \overline{X_2}}{s /\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$ , $S = \sqrt{\frac{n_1 s_1^2 + n_2 s_2^2}{n_1 + n_2 - 2}}$
C
$t = \frac{\overline{X_1} - \overline{X_2}}{S \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$ , $S = \sqrt{\frac{n_1 s_1^2 + n_2 s_2^2}{n_1 + n_2 - 2}}$
D
$t = \frac{\overline{X_1} + \overline{X_2}}{s \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$ , $S = \sqrt{\frac{n_1 s_1^2 + n_2 s_2^2}{n_1 + n_2 - 2}}$

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