Question

Body fluids were examined from Patients with a Chondrosarcoma over the time after initial treatment and remission. The levels of a particular chemotherapeutic drug were followed over a selected week. The "Nadir" or a minimum level was selected for analysis. Two weeks have been chosen for this analysis: one early in the treatment (Nadir 1); the other at the end of the treatment (Nadir 8)

Do the two nadirs differ? In particular, is Nadir 8 below Nadir 1? Use three test, one of which is parametric. Paired Data Problem

Subject	NADIR 1	NADIR 8
1	13.2	14
2	11.2	13.8
3	13.9	12.2
4	10.2	11.8
5	11.1	10.1
6	12.7	7.5
7	12	11.6
8	9.3	10.4
9	12.9	11.5
10	12.8	11.5
11	11.6	9.2
12	10.8	9.6
13	11.2	11.6
14	14.2	11.2
15	10.8	11.6
16	12.3	11.4
17	12.4	10.9
18	11.1	10.2
19	12.4	12.5
20	11.4	10.5
21	11.2	10.5
22	11.2	8.4
23	11.9	8.6
24	12.6	12
25	11.5	12.9
26	12	12
27	10.8	12
28	11.1	10.5
29	12	9.4
30	11.7	12

Answer 1

The hypothesis being tested is:

H0: µd = 0

Ha: µd ≠ 0

Subject	NADIR 1	NADIR 8	Difference
1	13.2	14	-0.8
2	11.2	13.8	-2.6
3	13.9	12.2	1.7
4	10.2	11.8	-1.6
5	11.1	10.1	1
6	12.7	7.5	5.2
7	12	11.6	0.4
8	9.3	10.4	-1.1
9	12.9	11.5	1.4
10	12.8	11.5	1.3
11	11.6	9.2	2.4
12	10.8	9.6	1.2
13	11.2	11.6	-0.4
14	14.2	11.2	3
15	10.8	11.6	-0.8
16	12.3	11.4	0.9
17	12.4	10.9	1.5
18	11.1	10.2	0.9
19	12.4	12.5	-0.1
20	11.4	10.5	0.9
21	11.2	10.5	0.7
22	11.2	8.4	2.8
23	11.9	8.6	3.3
24	12.6	12	0.6
25	11.5	12.9	-1.4
26	12	12	0
27	10.8	12	-1.2
28	11.1	10.5	0.6
29	12	9.4	2.6
30	11.7	12	-0.3
	11.7833	mean NADIR 1
	11.0467	mean NADIR 8
	0.7367	mean difference (NADIR 1 - NADIR 8)
	1.6765	std. dev.
	0.3061	std. error
	30	n
	29	df
	2.407	t
	.0227	p-value (two-tailed)

The p-value is 0.0227.

Since the p-value (0.0227) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the two nadirs differ.

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