Question

You are running a political campaign and wish to estimate, with 95% confidence, the proportion of registered voters who will vote for your candidate. Your estimate must be accurate within 3% of the true population. Find the minimum sample size needed if

1) No preliminary estimate is available

2) Preliminary estimate gives p (hat) = 0.31

3) Compare your results

Answer 1

Solution,

Given that,

a) =  1 - = 0.5

margin of error = E = 0.03

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 /0.03 )2 * 0.5 * 0.5

= 1067.11

sample size = n = 1068

b) = 0.31

1 - = 1 - 0.31 = 0.69

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

= (1.96 /0.03 )2 * 0.31 * 0.69

= 913.02

sample size = n = 914

c) Having an estimate of the population proportion reduces the minimum sample size is needed .