Question

Suppose you are given the following x and y values. Assume x is the independent variable and y the dependent variable.

x	y
13	10
10	11
3	4
29	23
5	8
25	21
8	10
17	15
19	17
31	29
23	24

Is there a significant relationship between x and y? Explain. Test at a 5% level of significance

Answer 1

	X	Y	X * Y
	13	10	130	169	100
	10	11	110	100	121
	3	4	12	9	16
	29	23	667	841	529
	5	8	40	25	64
	25	21	525	625	441
	8	10	80	64	100
	17	15	255	289	225
	19	17	323	361	289
	31	29	899	961	841
	23	24	552	529	576
Total	183	172	3593	3973	3302

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 11.9701

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 11.97014052 ) = 0.00000079
Reject null hypothesis if P value < level of significance
P - value = 0.00000079 < 0.05 ,hence we reject null hypothesis
Conclusion :- We reject H0

There is statistically sufficient evidence to conclude that there is linear relationship between x and y.