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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) andon 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
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.
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