Sampling variability and interval bands
A 95 percent confidence interval shows the range of plausible values for a population parameter, computed from a single sample. The diagram typically displays a sampling distribution (bell curve) with shaded bands marking the lower and upper bounds of the interval, often roughly two standard errors from the mean.
This is not the probability that the true parameter lies within this interval (it either does or doesn't). Instead, it represents the long-run frequency: if you repeated the study 100 times and computed a CI each time, roughly 95 of those intervals would contain the true parameter.
Visualizing repeated sampling and misses
Many confidence interval diagrams supplement the single-sample interval with a 'repeated sampling' panel showing 15 or 20 hypothetical samples and their computed intervals. One or two intervals typically fall outside the true parameter line, visually demonstrating the 5 percent miss rate.
This approach clarifies the frequentist logic: confidence refers to the procedure's long-run coverage rate, not the certainty of any single interval. It also shows why wider intervals (higher confidence) miss less often than narrow ones.