Minimum sample size n for for estimating the proportion within E percentage points. Of given C.L.=1-α

For proportion: given estimate p̂ (and thus q̂=1-p̂) or else 0.5 for both

p̂:    If no estimate known, use .5
desired E:    (is a proportion, i.e. between 0 and 1) e.g. for 3% enter .03
C.L.=1-α
90% Zc=1.645 95% Zc=1.96 98% Zc=2.326 99% Zc=2.576

n= Zc2 p̂q̂ / E2:round up
Population size N is irrelevant!

Exs. 

PROPORTION
If want 95% CL that E within .03 (3%) of p.  p̂=.79
If want 95% CL that E within .03 (3%) of p.  p̂ unknown thus .5

If want 99% CL that E within .03 (3%) of p.  p̂=.79
If want 99% CL that E within .03 (3%) of p.  p̂ unknown thus .5

Worksheet

  CL     E     p̂     n  
  95%     3%     .4  
  95%     3%     .5  
  95%     3%     .6  
  99%     3%     .4  
  99%     3%     .5  
  99%     3%     .6  
  95%     2%     .4  
  95%     2%     .5  
  95%     2%     .6  
  99%     2%     .4  
  99%     2%     .5  
  99%     2%     .6  

For a given C.L. and E, the largest minimum sample size n is when p̂=.

Minimum sample sizes decrease as p̂ and q̂ become more .

For a given E, a higher C.L. requires a minimum sample size.