On the Cost of not Knowing the Variance when Making a Fixed-Width Confidence Interval for the Mean
1. Summary. It is shown that the mean of a normal distribution with unknown variance amay be estimated to lie within an interval of given fixed width at a prescribed confidence level using a procedure which overcomes ignorance about awith no more than a finite number of observations. That is, the expected sample size exceeds the (fixed) sample size one would use if ar2 were known by a finite amount, the difference depending on the confidence level a but not depending on the values of the mean ,u, the variance 2 and the interval width 2d. A number of unpublished results on the moments of the sample size are presented. Some do not depend on an assumption of normality.