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What is the maximum sample size needed to estimate the proportion of adults in US who...

What is the maximum sample size needed to estimate the proportion of adults in US who vote regularly and want to be 95% sure that the error of our estimate will not exceed 0.06, if we have no information about the true proportion? (Answer should be rounded up to nearest integer)

Math   Statistics-And-Probability   
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Answer #1

solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.06

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96* 0.06)2 * 0.5 * 0.5

= 266.77

Sample size = 267 (rounded)

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