Q30: ‘Two samples of size n ate selected, one according to... - Numerical Analysis & Statistical Methods - Computer Application- ICAR JRF/SRF 2024 | Agrigyan

• Comparison of Variances in SRSWR and SRSWOR:
• Let $V_1$ be the variance of the sample mean based on all $n$ units under SRSWR:

• Let $V_2$ be the variance of the sample mean based on distinct units $d$ under SRSWR (using the Rao-Blackwellized estimator $\bar{y}_d$, where $E[d] \lt n$):

• Let $V_3$ be the variance of the sample mean under SRSWOR of the same fixed size $n$:

• Theoretical Ordering: Since repeated sampling adds redundant units in SRSWR, discarding duplicate units strictly improves efficiency ($V_1 \ge V_2$). Furthermore, a direct SRSWOR sample of fixed size $n$ always achieves at least as many distinct units as SRSWR, giving:

• Conclusion: The relationship that holds is $V_1 \ge V_2 \ge V_3$ (Option 1).

Correct option: (1) V42V22V3