Question: 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 \(\bar{x}=5.07 \mathrm{Mpa}\) and a standard deviation of \(s=.46 \mathrm{Mpa}\). Orthodontists want to know if the true mean breaking strength of the new bonding adhesive is less than \(5.70 \mathrm{Mpa}\), the mean breaking strength of the composite adhesive.

1. Set up the null and alternative hypothesis for the test.
2. Find the rejection region for the test using \(\alpha=.01\).
3. Compute the test statistic.
4. Give the appropriate conclusion for the test.
5. What conditions are required for the test results to be valid?

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