An occupant traffic study was carried out to aid in the remodeling of a large building on a university campus. The building has five entrances, and the choice of entrance was recorded for a random sample of 300 persons entering the building. The numbers of persons using Entrances 1, 2, 3, 4, and 5 were, respectively, 30, 91, 97, 40, and 42.
(1) Test the null hypothesis that the five entrances are equally used by setting α equal to .05.
(2) Find a 95 percent confidence interval for the proportion of all people who use Entrance 3.