statistics problem

Question

1. You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 19%. You would like to be 94% confident that your estimate is within 1% of the true population proportion. How large of a sample size is required?

Please round your z* value to 3 decimal places to use in your calculation.

n =

Answer 1

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

here p = 0.19

determining z*

confidence level in decimal = 0.94

critical probability = (1 + CL decimal)/2 = 0.97

z* = z-score for 0.97 probability = 1.881 (from table or using statistical calculator)

E given as 1% = 0.01 in decimal

sample size (n) = (0.19)*(0.81) * (1.881/0.01)^2 = 5445.23

round up to nearest integer = 5446