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 1% margin of error at a 99% 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 1% margin of error at a 99% confidence level.

Answer 1

Solution :

Given that,

= 0.5

1 - =0.5.

margin of error = E = 1% = 0.01

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

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

= (2.576 / 0.01)2 * 0.5 * 0.5

=16589.44

Sample size = 16589

if we take two decimal z value so answer is

= (2.58 / 0.01)2 * 0.5 * 0.5

=16641