In this activity, you will study the difference between binomial and multinomial experiments.

1. A television station has hired an independent research group to determine whether television viewers in the area prefer its local news program to the news programs of two other stations in the same city. Explain why a multinomial experiment would be appropriate and design a poll that satisfies the five properties of a multinomial experiment.

State the null and alternative hypotheses for the corresponding x² test.

2. Suppose the television station believes that a majority of local viewers prefer its news program to those of its two competitors. Explain why a binomial experiment would be appropriate to support this claim and design a poll that satisfies the five properties of a binomial experiment. State the null and alternative hypotheses for the corresponding test.

3. Generalize the situations in Exercises 1 and 2 to describe conditions under which a multinomial experiment can be rephrased as a binomial experiment. Is there any advantage in doing so? Explain.