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) 13.32 15.83 10.80 11.28 9.61 8.64 12.72 14.09 11.58 Lab B (y) 13.19 15.70 10.67 11.48 9.65 8.63 12.79 14.24 11.55 (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? 0.05 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

(A)

Compound	Lab A	Lab B	Rank(x)	Rank(y)	d = x-y	d2
1	13.32	13.19	7	7	0	0
2	15.83	15.70	9	9	0	0
3	10.80	10.67	3	3	0	0
4	11.28	11.48	4	4	0	0
5	9.61	9.65	2	2	0	0
6	8.64	8.63	1	1	0	0
7	12.72	12.79	6	6	0	0
8	14.09	14.24	8	8	0	0
9	11.58	11.55	5	5	0	0
Total					0	0

(b)

The level of significance is 0.05

The null and alternate hypotheses. H0: ρs = 0; H1: ρs ≠ 0

Sample test statistic =

= 1