I have this problem that I have been trying to figure out all week and can't seem to get. I have a process that produces one of two outcomes "OK" (in some unknown porportion: p) or "NOT OK" (in porportion q = 1-p). Lets say I ran the process [x] times (like 20) in a row and it reported "OK" each time. How can I calculated a 1-sided (or 2-sided) 95% confidence interval for the value of p? I think I should be assigning a value of "1" to "OK" and "0" to "NOT OK" and then applying the conventional confidence interval calculations using the t-distribution. The problem I run into is that all I observe are "OK" then my std deviation goes to 0 and the whole thing falls apart. Is there another method? What am I missing? Thanks, much appreciated.