Understanding t-Statistic in Regression Analysis

In a multiple regression analysis, an analyst is testing whether the coefficient for the independent variable $X_1$ is significantly different from zero. The null hypothesis ($H_0$) is that the coefficient for $X_1$ is equal to zero. The analyst finds that the estimated coefficient for $X_1$ is 2.3 with a standard error of 0.5. To determine if it is statistically significant at the 5% significance level, the analyst performs a t-test.

The test statistic for the t-test can be calculated using the formula:

$$ t = \f\frac{\hat{\beta}_{1}}{SE(\hat{\beta}_{1})} $$

Where:

- $\hat{\beta}_{1}$ is the estimated coefficient,

- $SE(\hat{\beta}_{1})$ is the standard error of the coefficient estimate.

What is the correct interpretation of the t-statistic calculated in this scenario?