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 1% margin of error at a 95% confidence level, what is the sample size that is needed? Give your answer as a whole number

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 1% = 0.01

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= (1.960 / 0.01)² * 0.5 * 0.5

= 9604

n = sample size = 9604