I am OK with part a, but I am having some troubles with part b.

Attempt for part b:

note: P(T>t_(n1+n2-2),alpha/2)=alpha/2 where T~t distribution with n1+n2-2 degrees of freedom.

Now, as n1 increases and n2 increases,

(i) t_(n1+n2-2),alpha/2 gets smaller

(ii) denominator gets larger

(iii) the ∑ terms gets larger because the upper indices of summation are n1 and n2, respectively

(i) and (ii) push towards a narrower confidence interval, but (iii) pushes towards a wider confidence interval. How can we determine the ultimate result?

Thank you for any help!

[note: also under discussion in sos math cyberboard]