I know that, but I see a few problems.
In part two do you really want a CI for
or
?
THEN, I think your instructor messed up with the relationship between the pop variances.
It works either way, but the algebra is nicer if we switch the 2 and the 3.
You start with the pt estimator that I already mentioned.
is unbiased for
and it's variance is
It's normal hence
Next use the relationship between the sigma's
BUT I keep asking, are they known?
If they are this is the test stat and you use a st normal table putting half of alpha in each table.
MORE likely the sigma's are unknown and you use the relationship and derive a t stat.
Here you need to pool the sample variances and obtain the chi-square distribution which replaces the
s