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## Homework Statement

http://www.geocities.com/asdfasdf23135/stat15.JPG

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

## Homework Equations

Width of a Confidence Interval

## The Attempt at a Solution

Attempt for part b:

http://www.geocities.com/asdfasdf23135/stat16.JPG

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?

Any help is greatly appreciated!