CI for µ when σ is known: simulation from normal (µ = 12, σ = 2)

This diagram shows that changing the constant k from 1.96 changes the proportion of CIs that include µ.

Click Accumulate and take 100 or more samples. Now adjust k.

Mention the following table and say that the constants are also used when estimating a proportion.

k Confidence level
1 0.683
2 0.954
3 0.997
1.645 0.90
1.960 0.95
2.576 0.99

When σ is unknown, say that changing the confidence level of a CI for µ involves looking up a different constant tn−1 from a table.