If I had a company of 5000 employees and wanted to be at least 99% sure to within +/- 3% that my survey results reflected the population... how many surveys would I need to administer?
To determine the number of surveys needed to achieve a certain level of confidence and margin of error, you can use the formula for calculating the sample size. The formula takes into account the population size, confidence level, and margin of error.
1. Start by determining the confidence level you desire. In your case, you mentioned wanting to be at least 99% confident, which corresponds to a confidence level of 0.99.
2. Next, determine the margin of error. A margin of error of +/- 3% means that you want the survey results to be within 3% of the true population value. In decimal format, this would be 0.03.
3. Now, you need to determine the population size. In your case, you mentioned having 5000 employees.
Once you have these values, you can calculate the sample size using the following formula:
Sample Size = (Z^2 * p * (1-p)) / E^2
Where:
Z = Z-score for the desired confidence level
p = estimated proportion of the population
E = margin of error
For a 99% confidence level, the Z-score is approximately 2.58. Using this value, we can calculate the sample size:
Sample Size = (2.58^2 * 0.5 * (1-0.5)) / (0.03^2)
First, we need to estimate the proportion of the population (p). Since you don't have an estimate, a conservative estimate is 0.5, which assumes an even distribution.
Sample Size = (2.58^2 * 0.5 * 0.5) / (0.03^2)
Sample Size = 664.536
Rounding up to the nearest whole number, you would need to administer approximately 665 surveys to achieve a 99% confidence level with a margin of error of +/- 3%.
Please note that the sample size assumes simple random sampling and certain assumptions about the population. Adjustments may be needed based on factors such as stratification, clustering, or finite population correction if applicable.