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
No. The student did not control the amount of free time, so the data only show correlation.
Yes. The student controlled the amount of free time, so the correlation implies causation.
No. The student did not control the grades, so the data only show correlation.
Yes. The student controlled the grades, so the correlation implies causation.
No. The student cannot conclude that more free time causes an improvement in grades based on correlation alone. Correlation only shows a relationship between the variables, but it does not prove causation. There could be other factors that are influencing both the amount of free time and the grades. Further research and analysis, such as experimental studies, would be needed to establish a causal relationship.
Which answer is it?
1,2,3, or 4
The correct answer is 1.
For example super smart students might be able to get good grades while spending less time on homework. That means brains --> more free time rather than more free time ---> better grades
That's a good example of an alternative explanation for the correlation between free time and grades. It highlights the importance of considering other factors that could explain the relationship between the variables.
The correct response is:
No. The student did not control the amount of free time, so the data only show correlation.
Explanation:
Correlation alone does not imply causation. In this case, the student only observed a correlation coefficient of 0.62 between the amount of free time and grades. This means that there is a positive relationship between the two variables, but it does not necessarily mean that more free time causes an improvement in grades. There could be other factors influencing the relationship, such as motivation, study habits, or other extraneous variables. To establish a causal relationship, the student would need to conduct a controlled experiment where they manipulate the amount of free time given to students and observe the effect on their grades.