In attempting to estimate μ from a simple random sample of size n, we previously employed the sample mean as a point estimator for μ, where a point estimator reports a single numerical value as the estimate of μ. Now, let us report a whole range of possible values rather than a single point estimate. This range of values is called an interval estimate or confidence interval for μ, that is, it is a range of values that enables us to state just how confident we are that the reported interval contains μ. What is the role of a confidence interval for μ? It indicates how precisely μ has been estimated from the sample; the narrower the interval, the more precise the estimate.

As we shall now see, we can view a confidence interval for μ as a “generalization of the error bound concept.” In this regard, we shall eventually determine our confidence limits surrounding μ as

(8.3)

where now the term ± error bound is taken to be our degree of precision.

Let us see how all this works. To construct a confidence interval for μ, we need to find two quantities L_{1} and L_{2} (both function of the sample values) such that, before the random sample is drawn,

where and are, respectively, lower and upper confidence limits for μ and is the ...

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