Statistical Inference: A Short Course

8.1 The Error Bound On As An Estimator Of

In the discussion that follows, we shall assume that the population variable X is or n is sufficiently large. (Why?) Then a 95% error bound on as an estimate of μ is

(8.1)

Once this error bound or maximum tolerable error level is calculated, we can conclude that: we are 95% confident that will not differ from μ by more than . Where did the 1.96 come from? As one might have guessed, it comes from the N(0, 1) area table (see Fig. 8.1). Using this process, the reader can easily verify that 90% and 99% error bounds on as an estimate of μ are and , respectively. ...