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.)

14        15

17        18

19        13

21        2

23        4

11        5

9          3

13        15

14        18

21        2

Answer 1

	X	Y	X * Y	X2	Y2
	14	15	210	196	225
	17	18	306	289	324
	19	13	247	361	169
	21	2	42	441	4
	23	4	92	529	16
	11	5	55	121	25
	9	3	27	81	9
	13	15	195	169	225
	14	18	252	196	324
	21	2	42	441	4
Total	162	95	1468	2824	1325

r = -0.2445

To Test :-
H0 :- ρ = 0
H1 :- ρ ≠ 0

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( -0.2445 * √(10 - 2) ) / (√(1 - 0.0598) )
t = -0.7132

Test Criteria :-
Reject null hypothesis if t > t(α,n-2) OR t < -t(α,n-2)
Critical value t(α/2,n-2) = t(0.05/2 , 10 - 2 ) = ± 2.306 ( From t table )
-2.306 < -0.7132 < 2.306
Result :- We fail to Reject null hypothesis

Decision based on P value
P - value = P ( t > 0.7132 ) = 0.496
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.496 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

There is insufficient evidence to support the claim that correlation coefficient between the two variables below differs significantly from 0.