Demonstration
This page demonstrates that 95% of confidence intervals do indeed include the population mean if they are obtained using the formula
where tn-1 is the value described on the previous page.
The diagram below shows a 95% confidence interval for µ based on a random sample of n = 20 values from a normal population with µ = 12.0 and σ = 2.0. The appropriate t-value for n = 20 is found by looking up a t-table with 19 degrees of freedom, t = 2.094.
Click Accumulate then click Take sample several times to select further samples.
Accumulate a display of 100 or more confidence intervals on the right of the diagram. Keep the mouse pressed on the Take sample button to repeatedly take samples.
Verify that approximately 95% of the confidence intervals do include the population mean, 12.0.