Chapter 4, Problem 16E

Two machines are used for filling glass bottles with a soft-drink beverage. The filling processes have known standard deviations al σ₁ = 0.010 liter and σ₂ = 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 ${\bar{x}}_1=2.04$ liters and ${\bar{x}}_2=2.07$ liters.

1. (a) Test the hypothesis that both machines fill to the same net contents, using α = 0.05. What are your conclusions?
2. (b) Find the P-value for this test.
3. (c) Construct a 95% confidence interval on the difference in mean fill volume.