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 94​% interval with a margin of error equal to .04 to estimate the proportion.

Answer 1

Answer:

Given,

To determine the additional number of voters that need to be sampled

n = 25

x = 21

Now consider,

p^ = x/n

substitute the values

p^ = 21/25

p^ = 0.84

q^ = 1 - p^

substitute p^ in q^

q^ = 1 - 0.84

q^ = 0.16

margin of error = 0.04

For 94% confidence interval , z value is 1.88

Now sample size = n = (Z/E)^2*p^*q^

substitute values

n = (1.88/0.04)^2 *0.84*0.16

= 296.8896

n = 297

Sample size = n = 297

The additional number of voters that need to be sampled = 297