Question

A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only wants a 0.1% margin of error at a 97.5% confidence level, what size of sample is needed?

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.1% = 0.001

At 97.5% confidence level the z is ,

= 1 - 97.5% = 1 - 0.975 = 0.025

/ 2 = 0.025 / 2 = 0.0125

Z_/2 = Z_0.0125 = 2.24

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

= (2.24 / 0.001)² * 0.5 * 0.5

= 1254400

Sample size = 1254400