Question

A certain region would like to estimate the proportion of voters who intend to participate in upcoming elections. A pilot sample of 50 voters found that 33
of them intended to vote in the election. Determine the additional number of voters that need to be sampled to construct a 99 % interval with a margin of error equal to 0.08

to estimate the proportion.

The region should sample ___ additional voters.

Answer 1

Answer: 183

Step-by-step explanation:

Given : A pilot sample of 50 voters found that 33 of them intended to vote in the election.

i.e. $\hat{p}=\dfrac{33}{50}=0.66$

and the voters sampled = 50

Significance level : $\alpha=1-0.99=0.01$

Critical value : $z_{\alpha/2}=2.576$

Margin of error:E = 0.08

The formula to find the sample size is given by :-

$n=\hat{p}(1-\hat{p})(\dfrac{z_{\alpha/2}}{E})^2\\\\\Rightarrow\ n=0.66(1-0.66)(\dfrac{2.576}{0.08})^2\\\\=232.666896\approx233$

Then, the additional voters need to be sample = $233-50=183$

Hence, the region should sample 183 additional voters.