A new dental bonding agent. Refer to the Trends in Biomaterials&Artificial Organs (Jan...

A new dental bonding agent. Refer to the Trends in Biomaterials&Artificial Organs (Jan. 2003) study of a new bonding adhesive for teeth, presented in Exercise: 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 , Jan. 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. Conduct the appropriate analysis for the orthodontists. Use a = .01 . Recall that the new adhesive (called “Smartbond”) has been developed to eliminate the necessity of a dry field. In one portion of the study, 30 extracted teeth were bonded with Smartbond and each was randomly assigned one of three different bonding times: 1 hour, 24 hours, or 48 hours. At the end of the bonding period, the breaking strength (in Mpa) of each tooth was determined. The data were analyzed with the use of analysis of variance in order to determine whether the true mean breaking strength of the new adhesive varies with the bonding time.

a. Identify the experimental units, treatments, and response variable for this design.

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b. Set up the null and alternative hypotheses for the ANOVA.

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c. Find the rejection region using α = .01.

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d. The test results were F = 61.62 and p-value ≈ 0. Give the appropriate conclusion for the test.

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