You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 35%. You would like to be 99% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required?
n=
= 0.35
1 - = 1 - 0.35 = 0.65
margin of error = E = 1% = 0.01
At 99% confidence level the z is,
= 1 - 99%
= 1 - 0.99 = 0.01
/2 = 0.005
Z/2 = 2.576
Sample size = n = (Z/2 / E)2 * * (1 - )
= (2.576 / 0.01)2 * 0.35 * 0.65
=15096
Sample size = 15096
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