A researcher wishes to estimate with 95 confidence the perce

A researcher wishes to estimate, with 95% confidence, the percentage of adults who support abolishing the penny. His estimate must he accurate within 5% of the true proportion. Find the minimum sample size needed, using a prior study that found that 22% of the respondents said they support abolishing the penny. No preliminary estimate is available. Find the minimum sample size needed. What is the minimum sample size needed using a prior study that found that 22% of the respondents said they support abolishing the penny n = What is the minimum sample size needed assuming that no prior information is available n =

Solution

a)

z value for 95% confidence = 1.96

n = (z * 0.05)^2 * p * q

n=( 1.96/0.05)^2 * (0.22)(0.78) = 263.68
n = 264 Answer when rounded up

b)

n = (z * 0.05)^2 * p * q

n=( 1.96/0.05)^2 * (0.5)(0.5) = 384.16
n = 385 Answer when rounded up