I am attempting to correctly interpret what a confidence interval means.

This is what I know: a confidence interval is a a continuous interval of values with a lower bound and an upper bound centered around a sample mean.For example given a certain population, we are interested in the true population mean and the 95% confidence interval CI:

- We can extract from the population N equal samples (all sample having identical size ##n##). Assume we pick N=100 samples.
- Each sample will have its own sample mean and its own sample standard deviation ##s##.
- Each sample will also generate its own confidence interval center at its own sample mean. The CI limits of each sample depends on standard deviation ##s## and the ##z## score we choose (the ##z## score value will determine if we talk about a 95% or 99% or 100% confidence interval). We pick ##z=1.96##.
- We end up with 100 samples and 100 confidence intervals. 95 among those 100 confidence intervals will contain the true population mean and 5 confidence intervals will surely not.
- The best estimate of the population mean is the average of the sample means. And as far as confidence interval...which confidence interval do we pick among the 95 CI that we are sure all contain the true population mean?