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Q59Section B (Part B)59 of 120

Unbiased estimator of the population mean under stratified sampling

Suppose we want to estimate the population mean Yˉ\bar Y of a variable for a finite population of size 8585, with 3434 Statisticians and 5151 Biologists. We consider the following sampling scheme:

A stratified random sample with 22 strata of Statisticians (Stratum-1) and Biologists (Stratum-2), where 1212 Statisticians and 1515 Biologists are drawn from Stratum-1 and Stratum-2, respectively, using SRSWOR scheme.

Denote yˉS\bar y_S, yˉB\bar y_B, and yˉ\bar y as the mean of the variable among the Statistician sample, Biologist sample, and the combined sample, respectively. Which of the following is an unbiased estimator of Yˉ\bar Y?

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