Final answer:
The correct answer is option b) False. The statement is false; a correlation near zero indicates no linear relationship between variables, but a non-linear or curvilinear relationship might still exist.
Step-by-step explanation:
A correlation coefficient near zero does not necessarily mean that no relationship exists between the variables; it simply means that there is no linear relationship. However, there could still be a curvilinear (non-linear) relationship present. For example, if you have a set of data that forms a perfect U-shape on a scatter plot, the correlation coefficient might be very close to zero, but there is clearly a relationship between the variables—it's just not linear. Therefore, saying a correlation near zero indicates no relationship at all is incorrect.
The correlation coefficient indicates the strength and direction of a linear relationship between two variables. A coefficient close to +1 or -1 indicates a strong linear relationship, while one close to 0 indicates a weak linear relationship. However, this doesn't address potential non-linear relationships that could exist between the variables.