9.3 A Confidence Interval for the Population Proportion (of Successes) p
As an alternative to simply using 
(determined from a simple random sample of size n taken from a binomial population) as a point estimator for p, let us determine a whole range of possible values that p could assume. This range of values is an interval estimate or confidence interval for p, that is, it is a range of values that allows us to state just how confident we are that the reported interval contains p. Once this interval is obtained, it enables us to state just how precisely p has been estimated from the sample; the narrower the interval, the more precise the estimate.
As will be indicated below, a confidence interval “generalizes the error bound concept.” In this regard, the confidence limits bounding p will be expressed as
(9.10) 
where the term ± error bound serves as our degree of precision.
To construct a confidence interval for p, we need to find two quantities L1 and L2 such that, before any sampling is undertaken,
where L1 and L2 are lower and upper confidence limits for p, respectively, and 1 − α is the confidence probability, which is chosen in advance. Once 1 − α is specified and L1
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