If you have a population of 500,000 people how many to be sampled to give a representative profile with only a 5% point margin of error ?
To determine the sample size needed to obtain a representative profile with a 5% margin of error, you can use a formula known as the sample size calculation for proportions.
The formula is:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n represents the desired sample size
- Z is the z-score corresponding to the desired level of confidence (usually 1.96 for a 95% confidence level)
- p is the estimated proportion of the population with the specific characteristic you want to measure (if unknown, use 0.5 for maximum variability)
- E is the desired margin of error, expressed as a decimal (in this case, 0.05 for a 5% margin of error)
Given that the population size is 500,000, the estimated proportion and margin of error, we can now calculate the sample size.
n = (1.96^2 * 0.5 * (1-0.5)) / 0.05^2
n = (3.8416 * 0.25) / 0.0025
n = 9.604 / 0.0025
n ≈ 3,841.6
Since you cannot have a fraction of a person in a sample, you would need to round up to the nearest whole number. Therefore, the sample size required to achieve a 5% margin of error in a population of 500,000 people would be approximately 3,842 individuals.