When bonding? teeth, orthodontists must maintain a dry field. A new bonding adhesive 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. Tests on a sample of 12 extracted teeth bonded with the new adhesive resulted in a mean breaking strength? (after 24? hours) of x overbar x=5.84 Mpa and a standard deviation of s=0.46 Mpa. Orthodontists want to know if the true mean breaking strength is less than 6.31 ?Mpa, the mean breaking strength of the composite adhesive.

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

b. Find the rejection region for the test using α=0.05

c. Compute the test statistic

d. Give the appropriate conclusion for the test