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 21 of them intended to vote in the election. Determine the additional number of voters that need to be sampled to construct a 98?% interval with a margin of error equal to 0.04 to estimate the proportion.

Answer 1

Solution :

Given that,

n = 25

x = 21

= x / n = 21 / 25 = 0.84

1 - = 1 - 0.84 = 0.16

Margin of error = E = 0.04

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

Sample size = (  Z_/2 / E)² * * (1 - )

= (2.326 / 0.04)² * 0.5 * 0.5

= 454.46 = 455

The additional number of voters that need to be sampled is = 455