Question

Consider a situation that a population of size M has been partitioned into to N primary u first stage, an unequal probability sample of n proportional to size (pt M/M) is taken fr its of sizes Mis. In the om primary units. In the second stage, e, an unequal probability sample of size m is selected from unit i and the variable of study un ary variable observed. The inclusion probability of unit j in primary unit i is my Derive, an or of, Hy, population mean, and its variance estimator when Ratio estimator used in the second stage.

Answer 1

sue Given (opulation Size . T unit in Sam ple th 76 5.th unit σ , thgroup (relude sampk. 0 it }th unit and過group isnot irelude in Sample populatis ulaon Man AV ovepall Populabon man tM ¡) N a) maands cluster) mean に, I

nH Then is an unbiased ahimata o perulaonm The vasiance oand its ebmates ae given by

Nn r)