A human resources manager at a large company wants to estimate the proportion of employees that would be interested in reimbursement for college courses. If she wishes to be 95% confident that her estimate is within 5% of the true proportion, how many employees would need to be samp
385
To estimate the required sample size for a proportion, we can use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n represents the sample size needed
- Z is the critical value corresponding to the desired confidence level (95% confidence level corresponds to Z = 1.96)
- p is an estimate of the true proportion in the population
- E is the desired margin of error
In this case, the HR manager wants to be 95% confident that her estimate is within 5% (0.05) of the true proportion. This means the margin of error desired (E) is 0.05.
Since the true proportion is unknown, we can conservatively assume that p = 0.5 (maximum uncertainty), which results in the largest sample size required.
Substituting the values into the formula, we have:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.05^2
Simplifying,
n = (3.84 * 0.25) / 0.0025
n = 0.96 / 0.0025
n = 384
Therefore, the HR manager would need to sample at least 384 employees in order to estimate the proportion of employees interested in reimbursement for college courses with 95% confidence and 5% margin of error.