problem-6.5
problem-6.5
The t distribution with 3 degrees of freedom has quite a long
tail. Because of this, it takes a large sample size for
\Xbar to have an approximately normal sampling distribution. The
following simulation should show that n=25 is large enough, as
measured by a q-q plot.
> res = c();for(i in 1:500) res[i] = mean(rt(25,3));qqnorm(res)
When n is much smaller than 25, the tails are still quite long.