If I ask people on the street if they prefer X to Y (true or false, a binary question). And they all independently respond X. At what stage could I infer that it is "highly likely" (which could be a 95% confidence interval) that most people prefer X if I have no idea what the population size is (I can not know how many people there are in total)?
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A confidence interval only makes sense in the context of hypothesis testing.
What's your null hypothesis that you hope to reject with statistical evidence? What's the alternative hypothesis?
With regard to the population and its size, what is the population? How are you sampling that population to make sure it is a good representation of the larger population? What uncertainty are you introducing by not being able to poll the entire population?
I know I've just given you five more questions instead of answering yours but these are the kinds of things you'll need to determine.
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$\begingroup$ The null hypothesis to test is irrelevant, but for clarity suppose I am testing whether chocolate tastes good. Where the alternative one is that it doesn't. The point of the question is that I have no idea about the population size, and want a trick to avoid this issue. $\endgroup$ Commented Aug 15, 2016 at 21:23