Question

members of a polling organization survey 700 of the 7,453 registered voters in a town by randomly choosing names from a list of all registered voters. Is there sample likely to be representative?

Answer 1

The sample is not representative. The minimum required is 716.

Explanation:

Data:

Poblation size (N) = 7,453

Error (e) = 5% = 0.05 (assumed)

Confidence level (CI)= 95% (assumed)

z-statisitc (z) = 1.96 (for CI = 95%)

Probability of success (p) = 0.5 (assumend)

Probability of no success (q) = 1 - 0.5 = 0.5

Minimum sample size required (n) = ?

`n=(N.z^(2).p.q.z )/([(n-1).e^(2)+p.q.z^(2)]  )`

`n=(7,453(1.96)^(2)(0.5)(0.5)(1.96) )/([(7,453-1)(0.05)^(2)+(0.5)(0.5)(1.96)^(2)]  )`

`n = (14,029)/(18.63+0.96)`

n = 716

The minimum amount of survey required to be representative is 716.

So the sample is not representative.

Hope this hepls!

Answer 2

Given:

Total sample size: 7,453 registered voters
*representative sample size = 700 registered voters

Assuming a confidence level of 95% and a margin of error of 3%, the sample of 700 voters is not representative. The sample size of 7,453 should have a representative sample of at least 934 voters.