In an experiment to compare two diets for fattening beef steers, nine pairs of animals were chosen from the herd; members of each pair were matched as closely as possible with respect to hereditary factors. The members of each pair were randomly allocated, one to each diet. The following table shows the weight gains (lb) of the animals over a 140-day test period on diet 1 (Y1) and
on diet 2 (Y2).
|
PAIR
|
DIET I
|
DIET 2
|
DIFFERENCE
|
|
1
|
596
|
498
|
98
|
|
2
|
422
|
460
|
-38
|
|
3
|
524
|
468
|
56
|
|
4
|
454
|
458
|
-4
|
|
5
|
538
|
530
|
8
|
|
6
|
552
|
482
|
70
|
|
7
|
478
|
528
|
-50
|
|
8
|
564
|
598
|
-34
|
|
9
|
556
|
456
|
100
|
Mean 520.4 497.6 22.9
SO 57.1 47.3 59.3
(a) Calculate the standard error of the mean difference.
(b) Test for a difference between the diets using a paired t test at α = 0.10. Use a nondirectional alternative.
(c) Construct a 90% confidence interval for μD.
(d) Interpret the confidence interval from part (c) in the context of this setting.