Question

Answer the correlation questions using the data below. Use α = 0.05.

x	y
3.1 3.9 5.9 7.1 6.1 4.9 7.2	4.5 5.1 5.9 6.6 5.1 4.9 5.9

a) Compute the correlation.
r =  

b) Compute the appropriate test statistic(s) for H₁: ρ > 0.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =  ;  ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

There is a significant positive relationship between x and y.There is a significant negative relationship between x and y.    There is no significant relationship between x and y.

Answer 1

b)

the appropriate test statistic(s) for H₁: ρ > 0

H₀: ρ = 0

H₁: ρ > 0

test stat :

t = r(sqrt(n-2)) / sqrt(1-r^2) = 3.4899

t critical = 2.015

t stat > t critical , Reject H0

c)

effect size r = +0.842

d)

There is a significant positive relation between x and y

Y2 x2 X X*Y 13.95 3.1 4.5 9.61 20.25 3.9 5.1 19.89 15.21 26.01 34.81 5.9 5.9 34.81 34.81 46.86 50.41 43.56 7.1 6.6 6.1 5.1 31.11 37.21 26.01 24.01 4.9 4.9 24.01 24.01 7.2 42.48 51.84 34.81 5.9 38.2 223.1 209.46 Sum 38 213.11

The correlation coefficient r is computed using the following expression: SSXY where 1 SSXY Xi Y3 n 2 1 Xi SSXX i=1 :() 1 Y2 SSyy Y3

In this case, based on the data provided, we get that 1 (38.2 x 38) = 5.739 SSxy 213.11 (38.2)2 14.637 SSXX 223.1 1 (38)2 = 3.174 SSyy = 209.46 - Therefore, based on this information, the sample correlation coefficient is computed as follows 5.739 SSXY 0.842 _ SSXX SSYY V14.637 x 3.174