Why do we check the 10% condition (n ≤ 0.10N) when sampling without replacement?

So that observations are approximately independent and the SD formula remains valid. With independence ensured by the 10% rule, σx̄ = σ/√n and σp̂ formulas are valid.

So that the sample is unbiased.

So that the population is normal.

So that observations are approximately independent and the SD formula remains valid.

Sampling Distributions for Sample Proportions

AP Statistics· difficulty 1/5

Why do we check the 10% condition (n \leq 0.10N) when sampling without replacement?

A
$So that the sample is unbiased.$
B
$So that the population is normal.$
C
$So that observations are approximately independent and the SD formula remains valid.$
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D
$So that p̂ equals p.$

Explanation

With independence ensured by the 10% rule, σ_x̄ = σ/\sqrtn and σ_p̂ formulas are valid.

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