Why is the 10% condition needed for SD(p̂) = √(p(1−p)/n)?

To allow assuming independence between sampled units (no replacement) Without replacement, dependence is negligible if n is much smaller than population.

To allow assuming independence between sampled units (no replacement)

Sampling Distributions for Sample Proportions

AP Statistics· difficulty 4/5

Why is the 10% condition needed for SD(p̂) = \sqrt(p(1-p)/n)?

A
$To enable CLT$
B
$To make p̂ unbiased$
C
$To allow assuming independence between sampled units (no replacement)$
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D
$To compute the mean$

Explanation

Without replacement, dependence is negligible if n is much smaller than population.

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