Answer: 272
Step-by-step explanation:
Given : A pilot sample of 25 voters found that 21 of them intended to vote in the election.
i.e. [tex]\hat{p}=\dfrac{21}{25}=0.84[/tex]
and the voters sampled = 25
Significance level : [tex]\alpha=1-0.94=0.06[/tex]
Critical value : [tex]z_{\alpha/2}=z_{0.03}1.88[/tex]
Margin of error: E = 0.04
The formula to find the sample size is given by :-
[tex]n=\hat{p}(1-\hat{p})(\dfrac{z_{\alpha/2}}{E})^2\\\\\Rightarrow\ n=0.84(1-0.84)(\dfrac{1.88}{0.04})^2\\\\=296.8896\approx297[/tex]
Then, the additional voters need to be sample = [tex]297-25=272[/tex]
Hence, the region should sample 272 additional voters.
