Title :   THE USE OF SAMPLE RANGES AND QUASI-RANGES IN SETTING EXACT CONFIDENCE BOUNDS FOR THE POPULATION STANDARD DEVIATION. I. THE RANGE OF SAMPLES FROM A RECTANGULAR POPULATION -- PROBABILITY INTEGRAL AND +ERCENTAGE POINTS; EXACT CONFIDENCE BOUNDS FOR SIGMA

Corporate Author : AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : HARTER,H.LEON

Report Date : MAY 1961

Pagination or Media Count : 1

Abstract : A discussion is given of point estimates and interval estimates of the population standard deviation sigma, 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 sigma are found by taking the reciprocals of percentage points of the standardized range W = w/V sigma. The following tables for the rectangular population are included: (1) An eight-decimal-place table of the probability integral of the range for W = 0.01(0.01)3.46 (0.001)3.464 and sample sizes n = 2(1)20(2)40(10) 100; (2) a six-decimal-place table of the percentage points of the range corresponding to cumulative probabilities P = 0.0001, 0.0005, 0.001, 0.005, 0.01, 0.025, 0.05, 0.1 (0.1) 0.9, 0.95, 0.975, 0.99, 0.995, 0.999, 0.9995, 0.9999 for the same values of n; and (3) a table of the coefficients of the sample range w in the exact lower confidence bounds for sigma for the above values of P and n. (Author)

Descriptors :   *STATISTICAL ANALYSIS, *STATISTICAL TESTS, ERRORS, PROBABILITY, STATISTICAL DISTRIBUTIONS, TABLES(DATA)

Distribution Statement : APPROVED FOR PUBLIC RELEASE