Question 1:

Hadey is selling a nutritional supplement that he claims will allow humans to oxygenate their blood more efficiently. To test his claim, Letecia randomly gathers 80 humans and randomly gives 40 of them the supplement and 40 of them a placebo. Then she asks all of them to run one mile and records their run times. If Hadey's claim is correct, the run times with the supplement should be LESS than those with the placebo she reasons. The first column in the Excel file "supplement.docx" is the runners with the placebo, the second column is those with the supplement. Test Letecia's claim at the 0.01 significance level.

Question 2:

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 Excel file 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