(Solution) - Suppose that 400 persons are chosen at random from a -(2025 Original AI-Free Solution)

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Suppose that 400 persons are chosen at random from a large population, and that each person in the sample specifies which one of five breakfast cereals she most prefers. For i = 1, . . . , 5, let pi denote the proportion of the population that prefers cereal i, and let Ni denote the number of persons in the sample who prefer cereal i. It is desired to test the following hypotheses at the level of significance 0.01:
H0: p1 = p2 = . . . = p5,
H1: The hypothesis H0 is not true.
For what values of would H0 be rejected?