Question

A political candidate has asked you to conduct a poll to
determine what percentage of people support her.

If the candidate only wants a 5% margin of error at a 95%
confidence level, what size of sample is needed?

Give your answer in whole people.

Answer #1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

Margin of error = E = 5% = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2} =
Z_{0.025} = 1.96

Sample size = ( Z_{/2} /
E)^{2} * * (1 - )

= (1.96 / 0.05)^{2} * 0.5 * 0.5

= 384.16 = 385

Sample size = n = 385

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