Mathematics · Probability and Statistics
A population of size N is divided into L strata of sizes N1, N2, ..., NL respectively. A stratified random sample of size n is drawn from the population where n1, n2, ..., n L denote the sam ple sizes in each of the L strata using simple random sampling within each stratum. Let ȳst = ∑ (Nj ȳj) / N and σst2 = V(ȳst). Consider an independent simple random sample of size n drawn from the total population with sample mean ȳ and variance σ2. Which of the following statements is correct under proportional allocation?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1If nj/Nj = n/N for all j, then σst2 = σ2
- 2The variance σst2 ≤ σ2✓
- 3The variance σst2 is always greater than σ2
- 4ȳst is a biased estimator of the population mean
Correct answer
The variance σst2 ≤ σ2
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