Question

A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. If the candidate wants a 1% margin of error at a 99% confidence level, what size of sample is needed? Be sure to round accordingly.

The candidate would need to survey ?????? people in the community in order to be within a 1% margin of error at a 99% confidence level.

Answer 1

Solution :

Given that,

= 0.5 ( assume 0.5)

1 - = 1 - 0.5 = 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 = 2.58    ( Using z table )

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

= (2.58 / 0.01)2 * 0.5 * 0.5

=16641

Sample size = 16641