Two machines are used for filling glass bottles with a soft-drink beverage. The filling processes have known standard deviations 1 = 0.010 liter and 2 = 0.015 liter, respectively. A random sample of n1 = 25 bottles from machine 1 and n2 = 20 bottles from machine 2 results in average net contents of x1 = 2.04 liters and x2 = 2.07 liters.
(a) Test the hypothesis that both machines fill to the same net contents, using = 0.05. What are your conclusions?
(b) Find the P-value for this test.
(c) Construct a 95% confidence interval on the difference in mean fill volume.