Question

Test for correlation between Barley and Corn prices using Spearman's rank correlation method, at the 0.05 significance level.

Barley	Rank	Corn	Rank	d	d^2
4.89	4	3.21	1	3	9
4.52	1	3.22	2	-1	1
4.85	2	3.29	4	-2	4
4.97	6	3.23	3	3	9
5.12	9	3.33	5	4	16
4.91	5	3.4	6	-1	1
5.08	8	3.44	8	0	0
4.98	7	3.49	9	-2	4
4.87	3	3.43	7	-4	16

Answer 1

Spearman rank's correlation

n : Number of pairs of data = 9

Barley	Rank	Corn	Rank	d	d2
4.89	4	3.21	1	3	9
4.52	1	3.22	2	-1	1
4.85	2	3.29	4	-2	4
4.97	6	3.23	3	3	9
5.12	9	3.33	5	4	16
4.91	5	3.4	6	-1	1
5.08	8	3.44	8	0	0
4.98	7	3.49	9	-2	4
4.87	3	3.43	7	-4	16
					d2=60

Null hypothesis : Ho : = 0 ; Correlation coefficient = 0

Alternate hypothesis : Ha : ; Correlation coefficient 0

Test statistic :

Test Statistic = 1.5275

Degrees of freedom = n-2=9-2=7

For two tailed test,

For 7 degrees of freedom, P(t>1.5275) = 0.0852

Given level of significance = 0.05

As p-value : 0.1705 > : 0.05; Fail to reject the null hypothesis;

There is not sufficient evidence to conclude that the correlation coefficient not equal to zero.