I have a finite space of 'data' (rows) that is fairly large (3 billion) and I want to check how many 'Positives' there are in this data set. However, checking the data is time consuming from a computational standpoint. If I have reason to believe that the data is i.i.d and each row has an equal likelihood of being a 'Positive' how can I calculate the sample size required to get a reasonable estimate on the TOTAL NUMBER (not just proportion in a Binomial Distribution) of 'Positives' in the data?
Things I have tried / other caveats:
I have looked into Binomial sample size calculation, but I'm not sure how this extends to the case where I am just looking for counts. I am guessing that when I multiply the estimated probability by the 3 billion, that it will distort the confidence intervals as it adds more variance.
I have looked into doing a Poisson sample size calculation but can't find many resources online that I can understand.
Do I have to assume that data is i.i.d in the distribution of 'Positives'? Intuitively I can understand why it wouldn't matter, since a large enough sample would factor in an aggregate probability of success.