Sample Sizes Confidence Intervals

Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 23%. You would like to be 99% confident that your estimate is within 4% of the true population proportion. How large of a sample size is required?

Answer 1

sample size = (p)(1-p) (z*/E)^2

here p = 0.23

determining z*

confidence level in decimal = 0.99

critical probability = (1 + CL decimal)/2 = 0.995

z* = z-score for 0.995 probability = 2.576 (from table or using statistical calculator)

E given as 4% = 0.04 in decimal

sample size (n) = (0.23)*(0.77) * (2.576/0.04)^2 = 734.5

round up to nearest integer = 735