Question

Calculate the t-test statistic for whether the correlation coefficient between the two variables below differs significantly from 0. (Hint: You will first need to calculate the correlation coefficient.)

5          6

4          3

3          2

5          6

6          8

7          9

8          11

9          9

1          4

14        13

Answer 1

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	5	6	1.4400	1.2100	1.3200
2	4	3	4.8400	16.8100	9.0200
3	3	2	10.2400	26.0100	16.3200
4	5	6	1.4400	1.2100	1.3200
5	6	8	0.0400	0.8100	-0.1800
6	7	9	0.6400	3.6100	1.5200
7	8	11	3.2400	15.2100	7.0200
8	9	9	7.8400	3.6100	5.3200
9	1	4	27.0400	9.6100	16.1200
10	14	13	60.8400	34.8100	46.0200
Total	62	71	117.6000	112.9000	103.8000
Mean	6.200	7.100	SSX	SSY	SXY

correlation coefficient r=		Sxy/(√Sxx*Syy)               =		0.901
test statistic:                t=		r*(√(n-2)/(1-r2))	=	5.869