27. Reconsider the CI (8.10) for p, and focus on a con dence level of 95%. Show that the con dence limits agree quite well with those of the traditional interval (8.11) once two successes and two failures have been appended to the sample [i.e., (8.11) based on (x  2) S s in (n  4) trials]. (Hint: 1.96  2.

Note: Agresti and Coull showed that this adjustment of the traditional interval also has actual con dence level close to the nominal level.)