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 p*= 82%. You would like to be 99% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required?

Answer 1

Hi Britt,

The formula for this sample size is:

n=(p*)(q*)(z_a/2/E)²

Let's break this down:

n=sample size we are looking for

p*=0.82

q*=1-p*=0.18

z_a/2=2.58 (99% is a relatively common confidence level; you can get 2.58 from the z-table, but I recommend memorizing this number for future problems that require 99% confidence. I also recommend memorizing 1.96 for problems requiring 95% confidence)

E=0.025 (Your acceptable error percentage converted to a decimal)

Substituting:

n=(0.82)(0.18)(2.58/0.025)²

n=1571.98

Rounding to nearest whole person:

n=1572

I hope this helps. Good luck.