If a sample of size 18 has a linear correlation coefficient

If a sample of size 18 has a linear correlation coefficient of -0.49 is there significant reason to conclude that the linear correlation coefficient of the population is negative? Use ? = 0.01.

Solution

Hypothesis:

Ho : r<0

Ha : r >0

degrees of freedom = 18 -2 = 16

critical value = t(0.01,16) = -2.92

test static = r * sqrt[ (n-2)/(1-r^2)]

= -0.49 * sqrt(16/1-0.49^2)

= -2.25

since test static is larger than critical value we fail to reject null hypothesis

hence there is no significant reason to conclude that the linear correlation coefficient of the population is negative