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Sample Size Formula
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Base Formula

n0 = (Z² × p × (1 − p)) / e²

Standard Cochran formula for large populations where sample proportion is known or estimated.

With Finite Correction

n = n0 / (1 + (n0 − 1) / N)

Used when the population is small and the sample size represents a significant portion of N.

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Calculation Parameters
{{-- Confidence Level --}}

Confidence Level (Z)

1.645 = 90%, 1.96 = 95%, 2.576 = 99%

@foreach(['90%' => 1.645, '95%' => 1.96, '99%' => 2.576] as $label => $val) @endforeach
{{-- Estimated Proportion --}}

Estimated Proportion (p)

Use 0.5 for most conservative estimate

@foreach(['10%' => 0.1, '30%' => 0.3, '50%' => 0.5] as $label => $val) @endforeach
{{-- Margin of Error --}}

Margin of Error (e)

Enter as decimal — 5% = 0.05

@foreach(['1%' => 0.01, '5%' => 0.05, '10%' => 0.1] as $label => $val) @endforeach
{{-- Population Size --}}

Population Size (N)

Optional
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Required Sample Size

385 units
Validated

Based on selected parameters

Label: Base formula used

Result Summary

Confidence Interval ± 5.0%
Confidence Level 95%
Standard Deviation 0.5