Null Hypothesis in Multiple Regression Analysis

In multiple regression analysis, a researcher is testing the hypothesis that there is no significant effect of two independent variables, $X_1$ and $X_2$, on a dependent variable $Y$. The null hypothesis ($H_0$) can be defined as:

$$H_0: \beta_1 = 0 \text{ and } \beta_2 = 0$$

To determine whether to reject the null hypothesis, the researcher calculates the F-statistic and compares it to the critical value from the F-distribution. If the F-statistic exceeds the critical value, the null hypothesis can be rejected. Which of the following statements is true regarding this hypothesis test?