we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days. How many randomly selected employers must we contact in order to create an extimate in which we are 98% confident , with an error of 5%
To estimate the percentage of businesses that plan to hire additional employees, you can use the formula for sample size calculation for proportion estimation.
The formula is:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = z-score corresponding to the desired confidence level (98% confidence level = 2.33 z-score)
p = estimated proportion (since you don't have an estimate, assume 50% for maximum variability, which gives the largest sample size)
E = margin of error (5% = 0.05)
Substituting the values into the formula:
n = (2.33^2 * 0.5 * (1-0.5)) / 0.05^2
n = (5.4289 * 0.25) / 0.0025
n = 10.8578 / 0.0025
n ≈ 4343.12
Therefore, you need to randomly select approximately 4343 employers to create an estimate with a 98% confidence level and an error of 5%. Since you cannot have a fraction of a respondent, rounding up to the nearest whole number means you should contact at least 4344 employers.