Chapter 4, Problem 24E

Two different types of glass bottles are suitable for use by a soft-drink beverage bottler. The internal pressure

strength of the bottle is an important quality characteristic. It is known that ${\sigma }_1={\sigma }_2=3.0$ psi. From a random sample of $n_1=n_2=16$ bottles, the mean pressure strengths are observed to be ${\bar{x}}_1=175.8$ psi and ${\bar{x}}_2=181.3$ psi. The company will not use bottle design 2 unless its pressure strength exceeds that of bottle design 1 by at least 5 psi. Based on the sample data, should they use bottle design 2 if we use $\alpha =0.05?$ What is the P-value for this test?