Reconsider the CI (7.10) for p, and focus on a confidence level of 95%. Show that the confidence limits agree quite well with those of the traditional interval (7.11) once two successes and two failures have been appended to the sample [i.e., (7.11) 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 confidence level close to the nominal level.]