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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?

Respuesta :

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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. 

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Answer:

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

Step-by-step 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) = ?  

[tex]n=\frac{N.z^{2}.p.q.z }{[(n-1).e^{2}+p.q.z^{2}]  }[/tex]

[tex]n=\frac{7,453(1.96)^{2}(0.5)(0.5)(1.96) }{[(7,453-1)(0.05)^{2}+(0.5)(0.5)(1.96)^{2}]  }[/tex]

[tex]n = \frac{14,029}{18.63+0.96}[/tex]

n = 716

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

So the sample is not representative.

Hope this hepls!

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