Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 24%. You would like to be 90% confident that your estimate is within 5% of the true population proportion. How large of a sample size is required?

Answer 1

Solution :

Given that,

= 0.24

1 - = 1 - 0.24 = 0.76

margin of error = E = 5% = 0.05

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= (1.645 / 0.05)2 * 0.24 * 0.76

=197.43

Sample size =198