Q46: When observations in two samples are paired and correlated (e.g.,... - Statistical Methods & Experimental Designs - ICAR AIEEA PG 2024 - Statistical Sciences | Agrigyan

For dependent/paired bivariate samples $(X_i, Y_i)$ of size $n$, the differences $d_i = X_i - Y_i$ are computed. The test statistic is:

where $\bar{d} = \frac{1}{n}\sum d_i$ and $s_d^2 = \frac{1}{n-1}\sum (d_i - \bar{d})^2$.
This follows Student's t-distribution with $(n - 1)$ degrees of freedom. Hence, Option 2 is correct.