Two different types of glass bottles are suitable for use by a softdrink beverag

Question

Two different types of glass bottles are suitable for use by a softdrink beverage bottler. The internal press strength of the bottleis an important quality characteristic. It is known thatsigma1=sigma2=3 psi. From a random sample of n1=n2=16 bottles. themean pressure strengths are observed to be xbar1=175.8 psiand xbar2=181.3 psi. The company will not use bottle design 2unless its pressure strength exceeds that of bottle design 1 by atleast 5 psi. Based on the sample data, should they use bottledesign 2 if we use alpha=.05? whats the p-value for this test?

Explanation / Answer

1=2=3 psi SE =(12/n1 + 22/n2) =(32/16 + 32/16) = 1.06 n1=n2=16 bottles xbar1=175.8 psi and xbar2=181.3 psi The company will not use bottle design 2 unless its pressurestrength exceeds that of bottle design 1 by at least 5 psi. Ho: 2 - 1 5 zcrit(=0.05, one-tail) = 1.64 zobs = ((xbar2 - xbar1) - (2 - 1))/SE =(181.3 - 175.8 - 5)/1.06 = 0.47 zobs = 0.05 fail to reject the null hypothesis, not sufficient evidencethat mean of design 2 does exceed mean of design 1 by at least 5psi. Use design 1.

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