1 answer

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you...

Question:

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=


Answers

\hat p = 0.35

1 - \hat p = 1 - 0.35 = 0.65

margin of error = E = 1% = 0.01

At 99% confidence level the z is,

\alpha = 1 - 99%

\alpha = 1 - 0.99 = 0.01

\alpha/2 = 0.005

Z\alpha/2 = 2.576

Sample size = n = (Z\alpha/2 / E)2 * \hat p * (1 - \hat p )

= (2.576 / 0.01)2 * 0.35 * 0.65

=15096

Sample size = 15096

.

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