Question

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

Answer 1

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

`n\text{ }\propto(1)/(E^2)`

that is

`\begin{gathered} n\text{ = }(k)/(E^2) \\ \text{Where k = constant of proportionality} \end{gathered}`

we are given

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

we get

`\begin{gathered} 58\text{ = }(k)/((0.1)^2) \\ 58\text{ }*(0.1)^2\text{ = k} \\ 58\text{ }*\text{ 0.01 = k} \\ k\text{ = 0.58} \end{gathered}`

Therefore the connection between n and E is

`n\text{ = }(0.58)/(E^2)`