Probability of proportions experiments

Binomial nominal data (i.e. counts of categories).
Exs: "Success"/"Failure" Yes/No Agree/Disagree Pass/Fail Defective/OK Good/Evil A/B

Population's categories' sizes:
Treat first as the #Successes (#1's).
Sample size n=
    


Population proportions:
The first is p (or π).

Sample proportions:    "Error"(sum of |diffs|):
The first is p̂.

Sample's categories' sizes:

Ex.
Pop is 60-40: 6000 4000
p=.6
Sample gives p̂

Pop cat sizes: 100 200 300 400
Sample size: 10 vs. 100