] Calculating a confidence interval does not guarantee that we will capture the true value of population parameter in the interval.
If we were to take considerable large number of samples (we only had one sample) and construct 95% confidence intervals for each of the samples we would expect about 95% of the confidence intervals to capture the the true value of population parameter in the interval.
- Sample statistics `\(\neq\)` population parameter.
- Different samples can have different statistics, thus there is sampling variability.
- We have constructed a confidence interval to infer about a median but we could do this for mean, proportion, difference between two group means etc.