Under certain conditions, electrical stimulation of a beef carcass will improve the tenderness of the meat. In one study of this effect, beef carcasses were split in half; one side (half) was subjected to a brief electrical current, and the other side was an untreated control. For each side, a steak was cut and tested in various ways for tenderness. In one test, the experimenter obtained a specimen of connective tissue (collagen) from the steak and determined the temperature at which the tissue would shrink; a tender piece of meat tends to yield a low collagen shrinkage temperature. The data are given in the following table.7
(a) Construct a 95% confidence interval for the mean difference between the treated side and the control side.
(b) Construct a 95% confidence interval the wrong way, using the independent-samples method. How does this interval differ from the one you obtained in part (a)?

Collagen shrinkage temperature CC) Curcass Treated side Control side Difference 1.25 0.25 Mean SD