The t-statistic isn't telling you very much about the stability of the
mean - rather it is telling you about the likely difference between
the intercept and zero.
However, this doesn't necesarily make any sense, for two reasons:
1. The intercept doesn't always make sense - the intercept is the
estimate of the value of the outcome variable, when all predictors are
equal to zero. If it is not possible for some, or all, predictors to
be zero, it's not worth considering the intercept out of context.
2. A transformation of the predictors can change the intercept - thsi
might happen if you change the reference category of a nominal
variable, or if you use a different zero point for your measure (many
measures have arbitrary zero points - e.g. earnings could use zero as
the zero, or could use the minimum wage, which is effectively zero).
If you are interested in the stability of the mean, I would consider
looking at the standard error.