The Use of Sample Ranges in Setting Exact Confidence Bounds for the Standard Deviation of a Rectangular Population
Abstract A discussion is given of point estimates and interval estimates of the population standard deviation σ, based on the sample range and quasi-ranges. In the case of a rectangular population, the efficient point estimate and the most effective interval estimates are those based on the sample range, so it is not necessary to consider estimates based on sample quasi-ranges. The coefficients of the sample range w in the exact confidence bounds for the population standard deviation σ are found by taking the reciprocals of percentage points of the (standardized) range W = w/σ. A six-decimal-place table of percentage points for the range corresponding to selected cumulative probabilities and sample sizes is presented. A second table shows coefficients of the sample range in exact lower confidence bounds.