Hadey argues that Letecia's test is unfair, because differences between individuals are large enough to overwhelm the effects of the supplement. He randomly gathers a sample of 40 humans and has them run a mile on two different days, randomly giving them either the supplement or a placebo on each day. The third column in the data represents the runners with the placebo, the fourth is the SAME runners with the supplement. Test Hadey's claim at the 0.01 significance level.

Data:

Letecia Placebo	Letecia Supplement	Hadey Placebo	Hadey Supplement
18.13	17.43	23.32	22.81
23.33	20.79	23.02	22.54
25.44	24.35	19.53	18.98
16.97	17.84	20.46	19.93
19.10	18.72	20.05	19.57
19.07	20.83	19.45	19.05
23.01	19.34	18.17	17.55
18.75	16.39	19.90	19.45
18.66	21.03	20.55	19.92
21.36	20.12	17.64	17.08
19.12	19.50	19.13	18.66
19.64	21.33	18.84	18.35
17.65	19.58	19.15	18.55
20.58	18.14	19.89	19.31
20.08	21.16	18.74	18.27
23.72	18.27	18.62	18.15
20.26	18.48	15.67	15.11
20.41	18.32	18.68	18.13
19.17	18.65	21.24	20.84
22.96	20.45	19.51	19.02
20.58	20.87	18.25	17.85
16.71	22.57	17.96	17.32
21.30	20.60	18.48	18.05
23.20	19.37	21.88	21.20
19.58	18.05	19.91	19.52
18.63	18.73	20.22	19.59
19.04	20.63	21.04	20.61
21.30	19.23	19.32	18.71
19.61	21.09	18.67	18.11
19.31	18.07	19.94	19.47
16.29	19.21	22.41	22.00
20.29	19.03	21.39	21.04
23.21	17.48	17.38	16.77
21.53	22.16	20.88	20.34
20.81	19.41	19.46	19.08
18.75	17.14	17.07	16.43
19.15	19.04	19.52	18.95
16.86	22.97	18.47	17.85
23.02	22.79	24.50	24.00
19.64	20.48	16.62	16.28