In the situation​ below, tell whether a correlation is likely. If it​ is, tell whether the correlation reflects a causal relationship. Explain your reasoning.

a person's shoe size and the number of times a person has failed the 6th grade.

Part 1
Is there likely to be a correlation in this situation. Choose the correct answer below.
A.
​Yes, there is likely to be a positive correlation in this situation.
B.
​Yes, there is likely to be a negative correlation in this situation.
C.
​No, there is not likely to be any correlation in this situation.

3 answers

C. No, there is not likely to be any correlation in this situation.

There is no logical connection between a person's shoe size and the number of times a person has failed the 6th grade. These two variables are unrelated and therefore, it is unlikely that there would be any correlation between them.
Part 2
Tell whether the correlation reflects a causal relationship. Explain your reasoning. Choose the correct answer below.

A.
There is not likely to be a correlation in the situation.

B. Since having bigger causes people to fail the 6th grade more often​, there is a causal relationship.

C. Since failing the 6th grade more often causes people to have bigger feet​, there is a causal relationship.
D.
Although there is a​ correlation, there is no causal relationship in the situation.
D. Although there is a correlation, there is no causal relationship in the situation.

There is no logical or scientific explanation to suggest that the size of a person's feet would have any impact on their academic performance or the number of times they fail the 6th grade. Therefore, while it is possible that a correlation may exist between shoe size and the number of times a person has failed the 6th grade, there is no evidence to suggest a causal relationship between the two variables.