Question

For their final statistics project, Jordynn and Angie surveyed a random sample of 50 students at their school. Each student in the survey reported his or her GPA and the number of pencils in his or her possession at the moment. The association between the number of pencils and GPA is linear, with a correlation of r = −0.23. Does the negative association suggest that carrying fewer pencils will increase a student’s GPA? Explain clearly.

Answer 1

Yes, the negative association suggests that carrying fewer pencils will increase a student's GPA.

Step-by-step explanation:

Yes, the negative association suggests that carrying fewer pencils will increase a student's GPA. When the correlation coefficient (r) is negative, it means that as one variable increases, the other variable tends to decrease. In this case, as the number of pencils in a student's possession decreases, their GPA tends to increase.

However, it's important to note that correlation does not imply causation. While there is a negative correlation between the number of pencils and GPA, carrying fewer pencils does not directly cause an increase in GPA. Other factors, such as study habits or motivation, may also contribute to a student's GPA.

Answer 2

The weak negative correlation of r = -0.23 between the number of pencils a student has and their GPA does not imply that carrying fewer pencils causes an increase in GPA; it simply indicates a slight association.

Step-by-step explanation:

The negative association indicated by the correlation of r = -0.23 between the number of pencils a student has and their GPA suggests that, on average, a student with fewer pencils has a slightly higher GPA. However, this is a weak negative correlation and does not imply causation. The correlation coefficient of -0.23 is close to 0, which means there is a weak relationship between the two variables. It is important to recognize the difference between correlation and causation. A correlation simply implies a relationship, not that one variable causes the other to change. To suggest that carrying fewer pencils will increase a student's GPA would be an incorrect interpretation of this data. There could be numerous unaccounted factors that influence a student's GPA.