Statistics: Confidence Intervals (Sample Size)

Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.11. You would like to be 96% confident that your esimate is within 5% 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 = 0.11

determining z*

confidence level in decimal = 0.96

critical probability = (1 + CL decimal)/2 = 0.98

z* = z-score for 0.98 probability = 2.054 (from table or using statistical calculator)

E given as 5% = 0.05 in decimal

sample size (n) = (0.11)*(0.89) * (2.054/0.05)^2 = 165.21

round up to nearest integer = 166