Use the Spearman's rank correlation coefficient at the 0.05 CI to investigate the relation between two...

Use the Spearman's rank correlation coefficient at the 0.05 CI to investigate the relation between two variables X and Y below.

X	Y
97	0
93	0
90	1
86	1
82	0
177	4
171	1
155	3
142	1
141	1
60	4
55	1
29	0
26	0
20	0
12	0
133	1
126	0
125	4
123	1
119	1
117	2

Expert Solution

X	Rank(X)	Y	Rank(Y)
97	11	0	4.5
93	10	0	4.5
90	9	1	13
86	8	1	13
82	7	0	4.5
177	22	4	21
171	21	1	13
155	20	3	19
142	19	1	13
141	18	1	13
60	6	4	21
55	5	1	13
29	4	0	4.5
26	3	0	4.5
20	2	0	4.5
12	1	0	4.5
133	17	1	13
126	16	0	4.5
125	15	4	21
123	14	1	13
119	13	1	13
117	12	2	18

	Rank(X)	Rank(Y)	*Rank(X)Rank(Y)**	Rank(X)²	Rank(Y)²
	11	4.5	49.5	121	20.25
	10	4.5	45	100	20.25
	9	13	117	81	169
	8	13	104	64	169
	7	4.5	31.5	49	20.25
	22	21	462	484	441
	21	13	273	441	169
	20	19	380	400	361
	19	13	247	361	169
	18	13	234	324	169
	6	21	126	36	441
	5	13	65	25	169
	4	4.5	18	16	20.25
	3	4.5	13.5	9	20.25
	2	4.5	9	4	20.25
	1	4.5	4.5	1	20.25
	17	13	221	289	169
	16	4.5	72	256	20.25
	15	21	315	225	441
	14	13	182	196	169
	13	13	169	169	169
	12	18	216	144	324
Sum =	253	253	3354	3795	3691

Conclusion: There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero.

orchestra answered 2 years ago

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