Question:Two different types of glass bottles are suitable for use by a soft drink beverage bottler. Internal pressure strength of the bottle is an important quality characteristic. It is known that σ1=σ2=3.0 psi. From a random sample of n1=n2=16 bottles, the mean pressure strengths are observed to be
X1_bar = 175.8 psi and X2_bar = 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 α= 0.05, What is the P-Value of the test?
Answers:
Z = (181.3-180.8)/ sqrt(3/16+3/16) = 0.82
p = 1- 0.2939 = 0.7061 (from normal table)
don't use the new bottles.
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