9.12 In industrial production processes, each measurable characteristic of any raw material must have some specified average value, but the variability should also be small to keep the characteristics of the end product within specifications. Samples of lead ingots to be used as raw material are taken from two different distributors; each distributor has a specification of median weight equal to 16.0 kg. The data below represent actual weight in kilograms.

X: 15.7, 16.1, 15.9, 16.2, 15.9, 16.0, 15.8, 16.1, 16.3, 16.5, 15.5 Y: 15.4, 16.0, 15.6, 15.7, 16.6, 16.3, 16.4, 16.8, 15.2, 16.9, 15.1

(a) Use the deviations from specified median weight to find two different interval estimates of sX=sY with confidence coefficient nearest 0.95.

(b) Use the method of positive variables to find a confidence-interval estimate of the ratio X=Y of scale measured relative to 0.