A large supermarket conducted a consumer preference study by recording the brand of wheat bread purchased by customers in its stores. The supermarket carries four brands of wheat bread. In a random sample of 200 purchasers, the numbers of purchasers preferring Brands A, B, C, and D of the wheat bread were, respectively, 51, 82, 27, and 40.
(1) Test the null hypothesis that the four brands are equally preferred by setting a equal to .05.
(2) Find a 95 percent confidence interval for the proportion of all purchasers who prefer Brand B.