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

Explanation:

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

i.e.
`\hat{p}=(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})((z_(\alpha/2))/(E))^2\\\\\Rightarrow\ n=0.66(1-0.66)((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.