Confidence intervals from pivots
This is an example of using a pivot to find a confidence interval.
1. Find a pivot.
Let
2. Find its distribution:
3. Find an expression involving an upper and lower bound on the pivot:
This implies
4. Substitute the expression for the pivot from Step 1, and set the RHS to
Let
This gives us
This was originally published here: https://calvinmccarter.wordpress.com/2013/11/06/confidence-intervals-from-pivots/