A sample of n 25 pairs of scores X and Y values produces a

A sample of n = 25 pairs of scores (X and Y values) produces a correlation of r = –0.40. Are these sample data sufficient to conclude that there is a significant non-zero correlation between X and Y in the population? Use a two-tailed test at the .05 level of significance.

Solution

As

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

Then

t = (-0.40)*sqrt((25-2)/(1-(-0.40)^2))

t = -2.093072474

Now, getting the critical t values at

df = n - 2 = 23

At 0.05 level, then

tcrit = 2.06865761

As |t| > tcrit, then there is a significant non-zero correlation between X and Y in the population. [CONCLUSION]