You would like to be 80% confident that you estimate is within 1.5% of the true population proportion. How large of a sample size is required?

Question

You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 80% confident that you estimate is within 1.5% of the true population proportion. How large of a sample size is required?

Answer 1

Hi Annie.

This is also a sample size calculation:

n=(z*/m)²*p*q

z*=z-critical value

m=margin of error

p=probability estimate

q=1-p

Now, we do not know anything about the population proportion, so we must estimate p=0.5. Next, the z=critical value for 80% confidence is 1.28. You may want to memorize if your instructor uses 80% confidence frequently. Thus:

z*=1.28

m=0.015 (1.5% as decimal)

p=0.5

q=0.5

n= (1.28/0.015)²*0.5*0.5

n= 1820.44

With minimum sample sizes, always round up to next whole number

n= 1821

I hope this helps.