Final answer:
The statement is false; a positive correlation means two variables increase or decrease together but doesn't necessarily indicate health benefits.
Step-by-step explanation:
True or False: A positive correlation means there are health benefits to the variable under investigation. This statement is False. A positive correlation simply indicates that two variables move in the same direction; as one variable increases, the other also increases, or as one decreases, the other also decreases. However, this does not inherently mean that there are health benefits to the variable under investigation. The positive correlation could relate to healthy habits, such as exercise and longevity, or it could correlate harmful substances to negative health outcomes, such as smoking and lung disease. It is the context of the correlation that determines whether the associated health outcomes are beneficial or detrimental.