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.

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Respuesta :

JeanaShupp JeanaShupp · Answer 1 · 2019-09-11T17:30:32+02:00

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. [tex]\hat{p}=\dfrac{33}{50}=0.66[/tex]

and the voters sampled = 50

Significance level : [tex]\alpha=1-0.99=0.01[/tex]

Critical value : [tex]z_{\alpha/2}=2.576[/tex]

Margin of error:E = 0.08

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=0.66(1-0.66)(\dfrac{2.576}{0.08})^2\\\\=232.666896\approx233[/tex]

Then, the additional voters need to be sample = [tex]233-50=183[/tex]

Hence, the region should sample 183 additional voters.