Question

A political candidate has asked you to conduct a poll to determine what percentage of people support her.

If the candidate only wants a 7% margin of error at a 99% confidence level, what size of sample is needed?

Give your answer in whole people.

Answer 1

Solution,

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 7% = 0.07

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

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

= (2.576 / 0.07)² * 0.5 * 0.5

= 338.56

Sample size = n = 339