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 an actual confidence level close to the nominal level.]
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