Question

A certain region would like to estimate the proportion of voters who intend to participate in upcoming elections. A pilot sample of 25 voters found that 18 of them intended to vote in the election. Determine the additional number of voters that need to be sampled to construct a 96​% interval with a margin of error equal to 0.07 to estimate the proportion.

Answer 1

Solution :

Given that,

=x/n = 18/25=0.72

1 - = 1 - 0.72 = 0.28

margin of error = E =0.07

At 96% confidence level the z is ,

Z/2 = 2.05   Using z table

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

= (2.05 / 0.07)2 * 0.72*0.28

= 172.9

=173 rounded