As the title says, I'm so confused by the concept. I've read so many explanations for the concept for the past few hours and I'm even confused than when I started, because a lot of the explanations seem to be contradictory.

R-bloggers states:

• It is not the probability that the true value is in the confidence interval.

• We are not 95% sure that the true value lies within the interval. (to me this means that we can't say with 95% confidence that the true value lies within the interval)

Here'sn example of several comments I've read that support these statements:

u/TokenStraightFriend

" Building off that because I only recently came to grips with what exactly "95% confident" means. It does NOT mean that there is a 95% chance that the true population average is within that range. Instead, if we were to repeat our sample taking, measuring, and averaging, we expect for 95% of the time the average height we find will be within that range we predescribed. "

Yet other comments contradict this

"So let's say you want to be 95% confident, so mostly certain, but with just a small degree of uncertainty. Then z=1.95, so we can say that the average population height is somewhere between 69-3(1.95) and 69+3(1.95) inches tall"

Is that not directly contradictory to what R-blogger states?

Here's an explanation from Eberly College of Science:

"

Rather than using just a point estimate, we could find an interval (or range) of values that we can be really confident contains the actual unknown population parameter. For example, we could find lower (L) and upper (U) values between which we can be really confident the population mean falls:

L < μ < U

And, we could find lower (L) and upper (U) values between which we can be really confident the population proportion falls:

L < p < U

"

Notice they say population and not sample. The distinction is made super clear in the Eberly college example.

I keep reading this idea that if you were to construct an infinite number of confidence intervals at a single confidence level 95%, 95% of those intervals may contain the true value for the parameter. That sort of explains what a confidence level is to me, but I don't understand when someone tells me 'this specific confidence interval has a confidence level of 95%'.