Formula for calculating sample size for unknown population
The formula for calculating sample size for an unknown population is:
n = [(Zα/2)² * p * (1-p)] / e²
Where:
n = sample size
Zα/2 = the critical value of the standard normal distribution at alpha/2 level of significance
p = the estimated proportion of the population with a particular characteristic
e = the maximum allowable error or margin of error
The value of Zα/2 depends on the level of confidence desired, p is the estimated proportion of the population with the characteristic of interest, and e is the allowed margin of error.
To calculate the sample size required for an unknown population, you can use the following formula:
n = (Z * Z * p * q) / E^2
where:
- n is the required sample size
- Z is the z-score corresponding to the desired confidence level (e.g., for a 95% confidence level, Z is approximately 1.96)
- p is the estimated proportion of the population with a certain characteristic (if unknown, you can use 0.5 as a conservative estimate to yield the largest sample size)
- q is the complement of p, which is calculated as 1 - p
- E is the desired margin of error (expressed as a proportion)
By using this formula, you can estimate the sample size needed to obtain a specific level of confidence and margin of error for an unknown population.