If Cov(X,Y)= - 16.0,variance of X = 25,variance of Y = 16 then the sample coefficient of correlation r is
A)+ 1.60
B)- 1.60
C)- 0.80
D)+ 0.80
E)Cannot be determined from the given information

Question

Quizplus · Accepted Answer

The formula for the sample correlation coefficient is:
r = Cov(X,Y) / (SD(X) * SD(Y))
where SD denotes standard deviation.

Using the given values, we have:
SD(X) = sqrt(variance of X) = sqrt(25) = 5
SD(Y) = sqrt(variance of Y) = sqrt(16) = 4

Substituting these values, along with Cov(X,Y) = -16, into the formula for r, we get:

r = -16 / (5 * 4) = -0.8

Therefore, the answer is option C) -0.80.