Which of the following represents a null hypothesis recognized by Julie?

The statement indicating that there is no difference in the rate of falls and the age of the patient accurately represents a null hypothesis. In hypothesis testing, the null hypothesis serves as a default position that indicates no effect, no relationship, or no difference exists between the variables being studied—in this case, the rate of falls and age.

The null hypothesis is often denoted as H0 and is crucial in statistical testing because it provides a baseline for comparison against the alternative hypothesis, which posits that there is a significant effect or relationship. In this context, stating that there is "no difference" effectively conveys the idea that any observed variations in fall rates across different ages could be due to random chance rather than a true underlying relationship.

In contrast, the other statements imply a relationship, effect, or difference. For instance, suggesting that there is a positive relationship between age and fall risk or that age directly influences fall risk both indicate an assumed interaction between age and fall incidents. Similarly, the assertion that younger patients experience fewer falls posits a directional relationship that does not fit the criteria for a null hypothesis.