In: Statistics and Probability
You want to obtain a sample to estimate a population proportion.
Based on previous evidence, you believe the population proportion
is approximately p∗=84%p∗=84%. You would like to be 95% confident
that your esimate is within 3% of the true population proportion.
How large of a sample size is required?
Solution :
Given that,
= 0.84
1 - = 1 - 0.84 = 0.16
margin of error = E = 3% = 0.03
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 ( Using z table )
Sample size = n = (Z/2 / E)2 * * (1 - )
= (1.96 / 0.03)2 * 0.84* 0.16
= 573.678
Sample size =574