I've been looking at numerous questions on this site regarding bootstrapping and confidence intervals, but I'm still confused. Part of the reason for my confusion is probably that I'm not advanced enough in my statistics knowledge to understand a lot of the answers. I'm about half-way through an introductory statistics course and my math level is only about mid-Algebra II, so anything past that level just confuses me. If one of the knowledgeable people on this site could explain this issue at my level it would be extremely helpful.
We were learning in class how to take resamples using the bootstrap method and use those to build up a confidence interval for some statistic we'd like to measure. So for example, say we take a sample from a large population and find that 40% say they'll vote for Candidate A. We assume that this sample is a pretty accurate reflection of the original population, in which case we can take resamples from it to discover something about the population. So we take resamples and find (using a 95% confidence level) that the resulting confidence interval ranges from 35% to 45%.
My question is, what does this confidence interval actually mean?
I keep reading that there's a difference between (Frequentist) Confidence Intervals and (Bayesian) Credible Intervals. If I understood correctly, a credible interval would say that there's a 95% chance that in our situation the true parameter is within the given interval (35%-45%), while a confidence interval would say that there's a 95% that in this type of situation (but not necessarily in our situation specifically) the method we're using would accurately report that the true parameter is within the given interval.
Assuming this definition is correct, my question is: What's the "true parameter" that we're talking about when using confidence intervals built up using the bootstrap method? Are we referring to (a) the true parameter of the original population, or (b) the true parameter of the sample? If (a), then we'd be saying that 95% of the time the bootstrap method will accurately report true statements about the original population. But how could we possibly know that? Doesn't the whole bootstrap method rest on the assumption that the original sample is an accurate reflection of the population it was taken from? If (b) then I don't understand the meaning of the confidence interval at all. Don't we already know the true parameter of the sample? It's a straightforward measurement!
I discussed this with my teacher and she was quite helpful. But I'm still confused.