Question

A statistics instructor wants to examine the relationship between the hours a student spends studying for the final (Hours) and a student’s grade on the final (Grade). She takes a sample of five students.

Student x (Hours) y(Grade)
1 8 75
2 2 47
3 3 50
4 15 88
5 25 93


Xbar = 10.6
Ybar = 70.6
sx = 9.6 sy = 21.2 sxy = 186.8

Compute the sample correlation coefficient.

Answer 1

The sample correlation coefficient is approximately 0.918, indicating a strong positive linear relationship between the hours spent studying and the final exam grade.

Step-by-step explanation:

To compute the sample correlation coefficient, we can use the formula r = sxy / (sx * sy), where sxy is the sample covariance, and sx and sy are the sample standard deviations of the x and y variables respectively. In this student's data set:

• sx = 9.6
• sy = 21.2
• sxy = 186.8

Now, we calculate the correlation coefficient:

r = 186.8 / (9.6 * 21.2) = 186.8 / 203.52 ≈ 0.918

The correlation coefficient of approximately 0.918 suggests a strong positive linear relationship between the number of hours spent studying and the final exam grade.