Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 73%. You would like to be 98% confident that your estimate is within 1.5% of the true population proportion. How large of a sample size is required?

Answer #1

Solution:

Given that,

= 73% =0.73

1 - = 1 - 0.73 = 0.27

margin of error = E = 1.5% = 0.015

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_{/2} = Z_{0.01} =
2.326

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

= (2.326 / 0.015)^{2} * 0.73 * 0.27

=4735.3275

= 4735

Large sample size required = 4735

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