instructor looked at his classes’ data from his first Mid Term. He recorded the students’ amount of study time (in minutes) and exam score (out of 100). He made a scatterplot and saw that it had a linear pattern. He computed correlation coefficient value or r = 0.81. After hearing about these results, one student concluded that if they study for a very long time, they will make very high test scores. What is wrong with this student’s interpretation?

Question

instructor looked at his classes’ data from his first Mid Term. He recorded the students’ amount of study time (in minutes) and exam score (out of 100). He made a scatterplot and saw that it had a linear pattern. He computed correlation coefficient value or r = 0.81. After hearing about these results, one student concluded that if they study for a very long time, they will make very high test scores. What is wrong with this student’s interpretation?

A. The teacher is using the wrong type of a plot therefore the results are invalid.

B. Since r = 0.81, you know the slope will be negative so studying a long time will give you a lower score.

C. The student is assuming that correlation implies causation i.e. just because there is an association between a higher test score and more number of study hours, doesn't mean every student who studies for long hours will get a high score.

D. All of the answers above are correct

I chose C I don't know if thats correct

Answer 1

Your choice of answer C is correct. The student's interpretation is flawed because they are assuming that correlation implies causation. Just because there is a positive association between the amount of study time and exam scores, represented by the positive correlation coefficient value of r = 0.81, it does not mean that studying for a very long time will guarantee very high test scores for every student.

Correlation coefficient measures the strength and direction of the linear relationship between two variables, in this case, study time and exam scores. A value of 0.81 indicates a strong positive correlation, meaning that as study time increases, exam scores tend to increase as well. However, it does not establish a cause-and-effect relationship. Factors other than study time, such as natural aptitude, test-taking skills, and individual learning abilities, can also influence exam scores.

Therefore, it is essential to understand that correlation does not imply causation. The student cannot assume that studying for a very long time will always result in very high test scores.