IBGE Analista Practice Questions - Concurso IBGE - Analista De Planejamento, Gestão E Infraestrutura Exam

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In survey sampling theory applied to IBGE household investigations, how does the variance of the sample mean under Simple Random Sampling Without Replacement (SRSWOR) compare to that under Simple Random Sampling With Replacement (SRSWR) for a finite population of size N and sample size n?

SRSWOR variance is strictly smaller by a factor of (N - n) / (N - 1), known as the finite population correction factor. SRSWOR variance is strictly larger because removing sampled elements reduces the degrees of freedom in subsequent draws. SRSWOR and SRSWR have identical theoretical variances because the sample mean remains an unbiased estimator in both designs. SRSWOR variance is smaller by a factor of (N - n) / N, but this reduction applies only when the sampling fraction exceeds 50%.

Correct Answer:

SRSWOR variance is strictly smaller by a factor of (N - n) / (N - 1), known as the finite population correction factor.

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