Final answer:
The statement that the correlation coefficient can be used on exponential graphs is false, as the correlation coefficient is designed for linear relationships, not for the non-linear relationships represented in exponential graphs.
Step-by-step explanation:
True or False: You can use the correlation coefficient on exponential graphs. This statement is false. The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. An exponential graph represents a non-linear relationship, and therefore, a linear correlation coefficient is not an appropriate measure. To analyze the relationship between variables on an exponential graph, other methods, such as nonlinear regression, should be used.
Correlation coefficient significance is determined by comparing it to critical values from statistical tables or by calculating a p-value. A positive correlation does not necessarily indicate health benefits; it simply reflects a direct relationship between two variables where they tend to increase or decrease together. The statement "A positive correlation means there are health benefits to the variable under investigation" is false. It's important to remember that correlation does not imply causation.