Two machines are used for filling glass bottles with a soft-drink beverage. The filling process have known standard deviations sigma(1) = 0.010 liter and sigma(2) = 0.015 liter, respectively. A random sample of n(1) = 25 bottles from machine 1 and n(2) = 20 bottles from machine 2 results in average net contents of x-bar = 2.04 liters and x-bar = 2.07 liters. a) Test the hypothesis that both machines fill to the same net contents, using alpha = 0.05. What are your conclusions? b) Find the P-value for this test. c) Construct a 95% confiedence interval on the difference in mean fill volume.