The estimated rate of loss of bags by American is:

pa=22/5000,

with sd:

sa=sqrt(pa(1-pa)/5000)

(as the number n lost is actualy ~b(n;5000,PA), where PA is the actual probability that A loses a bag which we estimate by pa).

The equivalent for Delta are:

pd=15/4000,

and

sd=sqrt(pd(1-pd)/4000).

Now you are expected to treat x=pa-pd as a normal random variable with standard deviation s=sqrt(sa^2+sd^2), and construct the 95% confidence interval for this. This is [(pa-pd)-1.96s,(pa-pd)+1.96s], if this interval does not include 0 we would construe this as supporting the idea that there is a difference in the bagage loss rates of the two airlines, otherwise that the difference is not statisticaly significant.

RonL