A probability Question on air-bags studies?

Question

In a study of air-bag effectiveness, it was found that in 821 crashes of midsize cars equipped with air-bags, 46 of the crashes resulted in hospitalition. Use a .01 significance level to test the claim that air-bag hospitaliztion rate is lower than the 7.8% rate for crashes of mid-size cars equipped with automatic safety belts.

Answer 1

I think that this is a binomial comparison of

pa air bag hospitalization
vs
ps seat belt hospitalization

But, n = 821 is large (np>30) allows use of normal approximation