Lauren conducted a one-sample $t$-test for a population mean and her results were found to be statistically significant at the $\alpha=0.05$ level.

Later, she realized that she had calculated the $p$-value using the wrong value for degrees of freedom, $\text{df}$. If the true $\text{df}$ should have been higher than the $\text{df}$ she had used in her calculation, would her results still be statistically significant?