Final answer:
A correlation coefficient of zero does not necessarily indicate independence between variables since they could still be dependent on each other in a non-linear way.
Step-by-step explanation:
In statistics, correlation measures the strength and direction of the relationship between two variables. A correlation coefficient of zero indicates no linear relationship between the variables. However, it does not necessarily mean that the variables are independent of each other.
Independence refers to the lack of any relationship or association between two variables. For example, if we flip two coins, the outcome of one coin flip does not affect the outcome of the other coin flip. In this case, the variables (coin flip outcomes) are independent of each other.
On the other hand, two variables can have no linear relationship but still be dependent on each other in a non-linear way. For instance, the number of hours spent studying and the test scores may have a correlation close to zero, indicating no linear relationship, but they are still likely to be dependent on each other. This is why a correlation coefficient of zero does not necessarily imply independence.