Part BCSIR NET June 2025stratum-weights-come-from-the-population-sizes-and-the-allocation-here-is-not-proportional

Stratum weights come from the population sizes and the allocation here is not proportional

Suppose we want to estimate the population mean Ȳ of a variable for a finite population of size 85, with 34 Statisticians and 51 Biologists. We consider the following sampling scheme: a stratified random sample with 2 strata of Statisticians (Stratum-1) and Biologists (Stratum-2), where 12 Statisticians and 15 Biologists are drawn from Stratum-1 and Stratum-2, respectively, using SRSWOR scheme. Denote ȳ_S, ȳ_B, and ȳ 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 Ȳ?

A.ȳ
B.(2ȳ_S + 3ȳ_B)/5✓
C.(4ȳ_S + 5ȳ_B)/9
D.(ȳ_S/12 + ȳ_B/15)/(1/12 + 1/15)

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests hypothesis dropped.

See pricing

50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

Stratum weights come from the population sizes and the allocation here is not proportional

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