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For a survey on a local referendum, the minimum necessary number of voters randomly polled n is inversely proportional to the square of the desired margin of error E. For a 0.1 (10%) margin of error, 58 voters must be polled. How many voters must be polled so that the margin of error is 2%?Blank voters

Respuesta :

From the question;

The number of voters randomly polled n is inversely proportional to the square of the desired margin of error E

This implies

[tex]n\text{ }\propto\frac{1}{E^2}[/tex]

that is

[tex]\begin{gathered} n\text{ = }\frac{k}{E^2} \\ \text{Where k = constant of proportionality} \end{gathered}[/tex]

we are given

when, E = 0.1 (10%), n = 58 voters

we get

[tex]\begin{gathered} 58\text{ = }\frac{k}{(0.1)^2} \\ 58\text{ }\times(0.1)^2\text{ = k} \\ 58\text{ }\times\text{ 0.01 = k} \\ k\text{ = 0.58} \end{gathered}[/tex]

Therefore the connection between n and E is

[tex]n\text{ = }\frac{0.58}{E^2}[/tex]

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