How large of a sample size is required?

Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 89%. You would like to be 80% confident that your estimate is within 3% of the true population proportion. How large of a sample size is required?

Answer 1

Hi Annie,

Our sample size formula for single proportion is:

n= (z*/m)²*p*q

z*=z-critical value

m=margin of error

p=probability estimate of "success"

q=1-p=probability estimate of "failure"

For our problem:

z*= 1.28 (check z-table; you may also want to memorize if your teacher uses 80% confidence a lot)

m=0.03 (3% as decimal)

p=0.89

q=0.11

n= (1.28/0.03)²*0.89*0.11

n= 178.22

When asked for minimum sample size, always round up because we do not wish to cut our sample size short, so:

n = 179

I hope this helps.