You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 95% confident that you esimate is within 4% of the true population proportion. How large of a sample size is required?
n=?
Do not round mid-calculation. However, use a critical value accurate to three decimal places.
Solution :
Given that,
= 0.5 ( assume 0.5)
1 - = 1 - 0.5= 0.5
margin of error = E = 4% = 0.04
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.960 ( Using z table )
Sample size = n = (Z/2 / E)2 * * (1 - )
= (1.960 / 0.04)2 * 0.5 * 0.5
= 600.25
Sample size =601
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