Question

Random collections of nine different solutions of a calcium compound were given to two laboratories, A and B. Each laboratory measured the calcium content (in mmol per liter) and reported the results. The data are paired by calcium compound. Compound 1 2 3 4 5 6 7 8 9 Lab A (x) 14.37 10.82 15.79 11.33 13.63 12.69 9.71 8.05 11.62 Lab B (y) 14.15 10.69 15.64 11.44 13.67 12.61 9.78 8.29 11.57 (a) Rank-order the data using 1 for the lowest calcium reading. Make a table of ranks to be used in a Spearman rank correlation test. Compound Lab A (x) Lab B (y) d = x − y d2 1 2 3 4 5 6 7 8 9 Σd2 = (b) Use a 5% level of significance to test for a monotone relation (either way) between ranks. Interpret the results. What is the level of significance? Correct: Your answer is correct. State the null and alternate hypotheses. H0: ρs = 0; H1: ρs < 0 H0: ρs ≠ 0; H1: ρs = 0. H0: ρs = 0; H1: ρs > 0 H0: ρs = 0; H1: ρs ≠ 0 Correct: Your answer is correct. Compute the sample test statistic. (Round your answer to three decimal places.)

Answer 1

x	y	Rx	Ry	d=Rx-Ry	d^2
14.37	14.15	8	8	0	0
10.82	10.69	3	3	0	0
15.79	15.64	9	9	0	0
11.33	11.44	4	4	0	0
13.63	13.67	7	7	0	0
12.69	12.61	6	6	0	0
9.71	9.78	2	2	0	0
8.05	8.29	1	1	0	0
11.62	11.57	5	5	0	0
					0
	∑d^2	0		ρ	1-(6*∑d^2/(n^3-n))
	n	9			1-(6*0/(9^3-9))
				ρ	1

Here ρ=1 means there is perfect positive correlation.

H0:ρ=0 vs H1:ρ>0