Question

Find the sample size needed to estimate the percentage of Independents (also referred to as “swing voters”) among the registered voters in Illinois. Since these votes could be crucial to winning the election, we want the error to be no more than 3% at a 95% confidence level. Assume p and q are unknown.

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= (1.96 / 0.03)2 * 0.5 * 0.5

= 1067.111

Sample size = 1068