11.67 When a surgeon repairs injuries, sutures (stitched knots) are used to hold together and stabilize the injured area. If these knots elongate and loosen through use, the injury may not heal properly because the tissues would not be optimally positioned.

Researchers at the University of California, San Francisco, tied a series of different types of knots with two types of suture material, Maxon and Ticron.

Suppose that 112 tissue specimens were available and that for each specimen the type of knot and suture material were randomly assigned. The investigators tested the knots to see how much the loops elongated.

The elongations (in mm) were measured and the resulting data are summarized here. For purposes of this exercise, assume it is reasonable to regard the elongation distributions as approximately normal.

Maxon Types of knot n x sd Square (control) 10 10.0 .1 Duncan Loop 15 11.0 .3 Overhand 15 11.0 .9 Roeder 10 13.5 .1 Snyder 10 13.5 2.0 Ticron Types of knot n x sd Square (control) 10 2.5 .06 Duncan Loop 11 10.9 .40 Overhand 11 8.1 1.00 Roeder 10 5.0 .04 Snyder 10 8.1 .06

a. Is there a significant difference in mean elongation between the square knot and the Duncan loop for Maxon thread?

b. Is there a significant difference in mean elongation between the square knot and the Duncan loop for Ticron thread?

c. For the Duncan loop knot, is there a significant difference in mean elongation between the Maxon and Ticron threads?