Thanks! But waht I'm asking is, if there is any practical consequense.
What I know is, when we appeal to large (asymptotic) sampal properties, we should use Z-test instead of t and Chi-square instead of F.
However, it seems to me that, practically few people use Z and Chi; and for most of the time, the test results of t and F are pretty close to Z and Chi. If this is the case, does that mean, the normality of error term is only a theoretial issue and we can actually ignore it in practice?