Final answer:
The statement that a positive correlation indicates health benefits is false. A positive correlation means that there is a relationship where both variables increase together, but this does not necessarily imply health benefits.
Step-by-step explanation:
The statement 'A positive correlation means there are health benefits to the variable under investigation' is false. A positive correlation simply means that as one variable increases, the other variable also increases. However, this does not inherently indicate that there are health benefits or positive outcomes associated with the variables.
For example, there could be a positive correlation between the amount of a certain junk food consumed and weight gain. In this case, the increase in both variables likely does not lead to health benefits.
Thus, the nature of the correlation (positive or negative) does not determine the health impact of the variables involved. It is essential to look at the context of the variables and understand the implications of their relationship.