A student is investigating if the amount of free time per week affects grades. He randomly surveys the students at his school and finds a linear relationship between the variables with a correlation coefficient of 0.62. Can the student conclude that more free time causes an improvement in grades? Explain.(1 point)

Question

A student is investigating if the amount of free time per week affects grades. He randomly surveys the students at his school and finds a linear relationship between the variables with a correlation coefficient of 0.62. Can the student conclude that more free time causes an improvement in grades? Explain.(1 point)

Responses

Yes. The student controlled the grades, so the correlation implies causation.
Yes. The student controlled the grades, so the correlation implies causation.

No. The student did not control the amount of free time, so the data only show correlation.
No. The student did not control the amount of free time, so the data only show correlation.

No. The student did not control the grades, so the data only show correlation.
No. The student did not control the grades, so the data only show correlation.

Yes. The student controlled the amount of free time, so the correlation implies causation.

Answer 1

No. The student did not control either variable, so the data only show correlation. The correlation coefficient of 0.62 indicates a moderate positive relationship between the two variables, but it does not prove causation. Other factors may be influencing both the amount of free time and grades, so it is not appropriate to conclude that more free time causes an improvement in grades based solely on the correlation coefficient. Further research, such as a controlled experiment, would be needed to determine causation.