When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called Smart bond) has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive may not stick to the tooth as well as the current standard, a composite adhesive. (Trends in Biomaterials & Artificial Organs, Jan. 2003.) Tests were conducted on a sample of 10 extracted teeth bonded with the new adhesive and a sample of 10 extracted teeth bonded with the composite adhesive. The Adhesive Remnant Index (ARI), which measures the residual adhesive of a bonded tooth on a scale of 1 to 5, was determined for each of the 20 bonded teeth after 1 hour of drying. An ARI score of 1 implies all adhesive remains on the tooth, and a score of 5 means none of the adhesive remains on the tooth. A breakdown of the number of bonded teeth in the five ARI categories is shown in the table.

a. Explain why the contingency table is one with fixed marginals.

b. Conduct an analysis to determine if the distribution of ARI scores differs for the two types of bonding adhesives. Use α = .05.

c. Are the assumptions of the test satisfied? If not, how does this impact the validity of the inference derived from the test?

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BONDING Adhesive Remnant Index Score 1 2 3 4 Smartbond 2 8 Composite 1 3 1