The percentage of a population that should be sampled for a survey can vary based on several factors, including the size of the population, the desired level of precision, and the confidence level you aim to achieve. However, a commonly referenced guideline in statistics is that a sample size of approximately 10-30% of the population is often sufficient to achieve reliable results, particularly if the population is large.
For smaller populations, you might need a higher percentage of the population to ensure that the sample adequately represents the whole group. Conversely, for larger populations, you can often achieve a good level of accuracy with a smaller percentage.
It's important to use formulas for determining sample size that take into account factors such as margin of error and confidence level, which often leads to needing sample sizes well below 10% of the population, especially if the population is large. For instance, a typical formula for calculating sample size in a survey is:
\[ n = \frac{N \times Z^2 \times p \times (1-p)}{E^2 \times (N-1) + Z^2 \times p \times (1-p)} \]
Where:
- \( n \) = required sample size
- \( N \) = population size
- \( Z \) = Z-value (from the Z-table, depending on confidence level)
- \( p \) = estimated proportion of the population (if unknown, use 0.5 for maximum sample size)
- \( E \) = margin of error
Always consider the specific context of your study when determining the necessary sample size.