Let us suppose that two independent random samples of sizes \(n_1\) and \(n_2\) has been drawn from the same normal population then degree of freedom of statistic t-distribution is.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(n_1 + n_2 - 2\)
To compare the two sample means, the t statistic uses the pooled variance of the two samples:
\( \displaystyle S^2 = \frac{\sum(x_1 - \bar{x}_1)^2 + \sum(x_2 - \bar{x}_2)^2}{n_1 + n_2 - 2} \)
Each sample loses one degree of freedom, because its own mean is estimated from it:
\((n_1 - 1) + (n_2 - 1) = n_1 + n_2 - 2\)
Note: This topic was not in the CUET 2026 syllabus.