Question

At the .05 significance level, does the data below show significant correlation?

x	y
5	21.1
6	25.22
7	29.34
8	16.26
9	15.18
10	20.9

• Yes, significant correlation
• No

Answer 1

Solution:

X	Y	XY	X^2	Y^2
5	21.1	105.5	25	445.21
6	25.22	151.32	36	636.0484
7	29.34	205.38	49	860.8356
8	16.26	130.08	64	264.3876
9	15.18	136.62	81	230.4324
10	20.9	209	100	436.81

n	6
sum(XY)	937.90
sum(X)	45.00
sum(Y)	128.00
sum(X^2)	355.00
sum(Y^2)	2873.72
Numerator	-132.60
Denominator	300.21
r	-0.4417
r square	0.1951
Xbar(mean)	7.5000
Ybar(mean)	21.3333
SD(X)	1.7078
SD(Y)	4.8829
b	-1.2629
a	30.8048

Therefore, the correlation coefficient r = -0.4417

df = n - 2 = 4

= 0.05

= 0.025

The critical value is = 0.811

Therefore, r = -0.4417 < 0.811, there is fail to reject the null hypothesis.

No, there is not significant correlation.