Question

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

x	y
1	19.97
2	18.16
3	27.55
4	15.34
5	25.43
6	26.22
7	12.11
8	11

• Yes, significant correlation
• No

Answer 1

X	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
1 2 3 4 5 6 7 8	19.97 18.16 27.55 15.34 25.43 26.22 12.11 11	12.250 6.250 2.250 0.250 0.250 2.250 6.250 12.250 Sum: 42.000	0.248 1.723 65.246 17.078 35.492 45.529 54.206 71.783 Sum: 291.304	-1.741 3.281 -12.116 2.066 2.979 10.121 -18.406 -29.654 Sum: -43.470

X Values
∑ = 36
Mean = 4.5
∑(X - M_x)² = SS_x = 42

Y Values
∑ = 155.78
Mean = 19.472
∑(Y - M_y)² = SS_y = 291.304

X and Y Combined
N = 8
∑(X - M_x)(Y - M_y) = -43.47

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -43.47 / √((42)(291.304)) = -0.393

A) null and alternate hypothesis

H0:=0

H1:0

B) test statistics

t = r√n-2/(1-r^2)

=( -0.393√(8-2))/(1-(-0.93)^2)

= -1.047

P value = 0.335

Conclusion

Since p value is greater than level of significance so we reject H0.

So there insufficient evidence to conclude that there significant relation between x and y

Ans No