Question

Clyde is a political candidate. Clyde asks Marge, his head of polling, to conduct a poll that will estimate the percentage of voters who support him with a 2% margin of error at a 95% confidence level. How many random voters does Marge need to poll? Be sure to round accordingly. Marge would need to survey voters in order to be within a 2% margin of _______ error at a 95% confidence level.

Answer 1

Solution :

Given that,

= 0.5 ( assume 0.5

1 - = 1 - 0.5= 0.5

margin of error = E = 2% = 0.02

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.02)2 * 0.5 * 0.5

= 2401

Sample size =2401