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.
|
CARCASS
|
COLLAGEN SHRINKAGE TEMPERATURE (°C)
|
|
TREATED SIDE
|
CONTROL SIDE
|
DIFFERENCE
|
|
1
|
69.50
|
70.00
|
-0.50
|
|
2
|
67.00
|
69.00
|
-2.00
|
|
3
|
70.75
|
69.50
|
1.25
|
|
4
|
68.50
|
69.25
|
-0.75
|
|
5
|
66.75
|
67.75
|
-1.00
|
|
6
|
68.50
|
66.50
|
2.00
|
|
7
|
69.50
|
68.75
|
0.75
|
|
8
|
69.00
|
70.00
|
-1.00
|
|
9
|
66.75
|
66.75
|
0.00
|
|
10
|
69.00
|
68.50
|
0.50
|
|
11
|
69.50
|
69.00
|
0.50
|
|
12
|
69.00
|
69.75
|
-0.75
|
|
13
|
70.50
|
70.25
|
0.25
|
|
14
|
68.00
|
66.25
|
1.75
|
|
15
|
69.00
|
68.25
|
0.75
|
|
Mean
|
68.750
|
68.633
|
0.117
|
|
SD
|
1.217
|
1.302
|
1.118
|
(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)?