Final answer:
The statement is False, as a positive correlation does not inherently indicate health benefits but merely a relationship where two variables move in the same direction. Health effects can vary based on the specific context of the correlated variables.
Step-by-step explanation:
The statement that a positive correlation means there are health benefits to the variable under investigation is False. A positive correlation simply indicates that two variables move in the same direction, meaning when one variable increases, the other one also increases, or when one decreases, the other one also decreases. However, this does not imply that an increase in the variable necessarily leads to health benefits. The effect on health can be neutral, negative, or positive depending on the nature of the variables involved. To accurately determine health benefits, one would have to look at the specific context and details of the variables being studied. For instance, a positive correlation between exercise and heart health does suggest a beneficial relationship, but a positive correlation between cigarette smoking and lung cancer indicates a detrimental one.