A new dental bonding agent. When bonding teeth, orthodontists must maintain a dry field. A...

A new dental bonding agent. When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called “Smartbond”) has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. (Trends in Biomaterials &  Artificial Organs, January 2003.) Tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of  Mpa and a standard deviation of s = .46 Mpa, where Mpa = megapascal, a measure of force per unit area. Orthodontists want to know if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, the mean breaking strength of the composite adhesive.

a. Set up the null and alternative hypotheses for the test.

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b. Find the rejection region for the test, using α = .01.

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c. Compute the test statistic.

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d. State the appropriate conclusion for the test.

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e. What conditions are required for the test results to be valid?