# Adding coefficients to obtain interaction effects – what to do with SEs?

I have a multivariate regression, which includes interactions. For example, to get the estimate of the treatment effect for the poorest quintile I need to add the coefficients from the treatment regressor to the coefficient from the interaction variable (which interacts treatment and quintile 1). When adding two coefficients from a regression, how does one obtain standard errors? Is it possible to add the standard errors from the two coefficients? What about the t-stats? Is it possible to add these as well? I’m guessing not but I can’t find any guidance on this.

I think this the expression for $SE_{b_{new}}$:
You can work with this new standard error to find your new test statistic for testing $H_o: \beta=0$