Bon Appetit magazine polled 200 of its readers concerning which of the four vegetables-brussel sprouts, okra, lima beans, and cauliflower-is their least favorite. The results

(adapted from Adweek, Feb. 21, 2000) are presented in the table. Let p,, p2, p,, and p, represent the proportions of all Bon Appetit readers who indicate brussel sprouts.

okra, lima beans, and cauliflower, respectively, as their least favorite vegetable.

a BONAPP.DAT ..............................................................................................................

Brussel Sprouts Okra Lima Beans Cauliflower ..............................................................................................................

46 76 44 34

a. If in general, Bon Appetit readers do not have a preference for their least favorite vegetable, what are the values of PI, p2, P,, and p4?

b. Specify the null and alternative hypotheses that should be used to determine whether Bon Appetit readers have a preference for one of the vegetables as "least favorite."

c. Conduct the test you described in part b using a = .05.

Report your conclusion in the context of the problem.

d. What assumptions must hold to ensure the validity of the test you conducted in part c? Which, if any, of these assumptions may be a concern in this application?