If my counts are from a proportion (resampling) of a sample, does it influence the confidence interval? The aim is to estimate the proportion (or counts) of a certain species among a collected sample. Due to the large number, it is not possible to count through the whole sample. So I have to select a proportion of the sample (roughly divide the sample by size or weight), for instance 1/3 of this sample. My question is: will this extra resampling influence the confidence interval of the estimated proportion for this species? especially if the species is rare (proportion is almost 0)? Is there any analytical interpretation?
Thanks 
 A: I wouldn't refer to this situation as "resampling", a term which has a technical meaning in statistics.  If you took a sample, then took a random sample of that, you still have a sample that is as representative of your population as before, just with a smaller $N$.  So long as you use the appropriate $N$ (i.e., the smaller one), no problems will arise.  
On a different note, I don't fully follow your situation, but if your "counts" are just $1$ or $0$ for each case, then you should realize that you are dealing with Bernoulli trials rather than counts.  We typically refer to data as counts if it is possible for the values to be any natural number $[0, +\infty)$, whereas is is only possible for the 'counts' from $N$ Bernoulli trials to be $[0, N]$.  These facts have some important implications: if you are dealing with true counts, you would analyze your data with some form of Poisson regression, whereas if your data are the outcomes of Bernoulli trials, you would use some form of logistic regression.  
