Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 16%. You would like to be 90% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required? Do not round mid-calculation.

n =

Answer 1

Solution :

Given that,

= 0.16

1 - = 1 - 0.16= 0.84

margin of error = E = 3% = 0.03

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )   

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

= (1.645 / 0.03)² * 0.16 * 0.84

=404

Sample size = 404