Rose believes there is a positive correlation between watching violence on television and aggressive behavior. what would be her null hypothesis?

When testing a hypothesis using a null hypothesis, you use a statement that negates your hypothesis, and, within a certain level of certainty, see if the null hypothesis can be rejected. When testing the null hypothesis, you typically want to be around 95% sure that you can reject it (confidence interval is 95%). 

In Rose's case, she is testing the hypothesis that there is a correlation between watching violence on television and aggressive behavior.

Her null hypothesis would be:
"There is not a positive correlation between watching violence on television and aggressive behavior"
or
"The correlation between watching violence on television and aggressive behavior is less than or equal to zero"

Correct textbook answers would be 1,3, and 5