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 17 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 0.05 to estimate the proportion.

Answer 1

Solution :

Given that,

n = 25

x = 17

= 17 / 25 = 0.68

1 - = 1 - 0.68 = 0.32

Margin of error = E = 0.05

At 96% confidence level the z is ,

= 1 - 96% = 1 - 0.96 = 0.04

/ 2 = 0.04 / 2 = 0.02

Z_/2 = Z_0.02 = 2.054

Sample size = (Z_/2 / E)² * * (1 - )

= (2.054 / 0.05)² * 0.68 * 0.32

= 367.21 = 368

The additional number of voters that need to be sampled is 368 .