अंतर-मूल्यांकनकर्ता विश्वसनीयता कैलकुलेटर — सूत्र
## How to Calculate Sample Size
The sample size formula balances precision against cost. A larger sample reduces the margin of error but requires more resources.
### Formula (Cochran's)
**n_0 = Z^2 x p x (1 - p) / E^2**
With finite population correction:
**n = n_0 / (1 + (n_0 - 1) / N)**
Where Z is the z-score for your confidence level, p is the expected proportion, E is margin of error, and N is population size.
Using p = 0.5 gives the most conservative (largest) sample size when the true proportion is unknown.
The sample size formula balances precision against cost. A larger sample reduces the margin of error but requires more resources.
### Formula (Cochran's)
**n_0 = Z^2 x p x (1 - p) / E^2**
With finite population correction:
**n = n_0 / (1 + (n_0 - 1) / N)**
Where Z is the z-score for your confidence level, p is the expected proportion, E is margin of error, and N is population size.
Using p = 0.5 gives the most conservative (largest) sample size when the true proportion is unknown.
हल किया गया उदाहरण
A researcher needs 95% confidence (Z = 1.96), 5% margin of error, expected proportion 0.5, population 10,000.
- n_0 = 1.96^2 x 0.5 x 0.5 / 0.05^2 = 3.8416 x 0.25 / 0.0025 = 384.16
- Finite correction: 384.16 / (1 + 383.16 / 10000) = 384.16 / 1.0383 = 370
- Required sample size: 370