Question

How many voters should be sampled for a 95% confidence interval? Round up to the nearest whole number.

Answer 1

467 voters

Explanation:

Given

See attachment for complete question

Required

Sample size at 95% confidence interval

From the attachment, we have:

`p = 65\% = 0.65`

`E = 4.33\% = 0.0433`

`CL = 0.95`

`\alpha = 0.05` i.e. 1 - CL

First, we calculate the critical level

At
`CL = 0.95` and
`(\alpha)/(2)`

`z^* = 1.96` --- the critical level

So, we have:

`n = p * (1 - p) * ((z^*)/(E))^2`

`n = 0.65 * (1 - 0.65) * ((1.96)/(0.0433))^2`

`n = 0.65 * (1 - 0.65) * (45.3)^2`

`n = 0.65 * 0.35 * 2052.1`

`n = 466.9`

`n = 467` --- approximated