Properties of 95% CI
As with earlier confidence intervals, the 95% CI for σ is random and varies from sample to sample.
Simulation
The diagram below shows random samples from a normal population with standard deviation σ = 2.0.
The 95% CI for σ is shown on the right. Click Accumulate then take several samples to observe the variability of the 95% CIs. After taking over 100 samples, observe that:
Approximately 95% of the CIs include the population standard deviation, 2.0.