Question

Your boss asked you to mail surveys to residents of Calico County (Population: 50,000) on a regional park project. To have 95% confidence interval and +/-3% margin of error in your mail survey in Calico County, you need to have at least ___________________ responses back.

Answer 1

At 95% confidence level, the critical value is z0.025 = 1.96

Margin of error = 0.03

Or, z0.025 * sqrt(p(1 - p)/n) = 0.03

Or, 1.96 * sqrt(0.5(1 - 0.5)/n) = 0.03

Or, n = (1.96 * sqrt(0.5 * 0.5)/0.03)^2

Or, n = 1068