Explain why the t-statistic helps

Suppose you estimate an effect size \(\hat{\beta}\) in a regression model or an A/B test and compute a standard error \(SE(\hat{\beta})\). Explain why the t-statistic \[ t = \frac{\hat{\beta}}{SE(\hat{\beta})} \] is often a useful summary of evidence. What does it capture that the raw coefficient or mean difference does not? Discuss how it connects to p-values and confidence intervals, what assumptions are required, and in what situations relying on the t-statistic can be misleading.