Question

A random sample for 11 scores produced the following(hours of study, grade) data values.

Hours STudied(X) 10 3 9 4 9 3 1 10 6 3 4
Test Grade(Y) 98 55 89 74 95 56 45 92 89 60 75
a. Compute the covariance.
b. Compute the correlation coefficient.

Answer 1

To calculate the covariance, use the formula involving the means of hours studied and test grades, then divide the sum by n-1. For the correlation coefficient, divide the calculated covariance by the product of the standard deviations of hours studied and test grades.

Step-by-step explanation:

To solve for the covariance and correlation coefficient using the given data of hours studied (X) and test grades (Y), we first need to calculate the means of both X and Y. After that, we'd use the formula for covariance:

Cov(X, Y) = Σ[(X_i - μ_X)(Y_i - μ_Y)] / (n - 1)

where μ_X and μ_Y are the means of X and Y, X_i and Y_i are the individual sample points, and n is the number of sample points. We would then calculate the standard deviations of both X and Y and use them along with the covariance to compute the correlation coefficient:

r = Cov(X, Y) / (σ_X σ_Y)

Where r is the correlation coefficient, σ_X is the standard deviation of X, and σ_Y is the standard deviation of Y. The value of r ranges from -1 to 1, indicating the strength and direction of the linear relationship between X and Y.