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"