Question

Researchers were interested in conducting a taste on three different sodas: coke, pepsi, and Dr.pepper.The researchers asked 100 people to try all three and pick their favorite soda. 1)what type of model should the researcher use as their known population.

Answer 1

The follwoing can be a reasonable model:

Let p1, p2, p3 be the respective probabilities that Coke, Pepsi and Dr.Pepper is the favourite among the three respectively. (where p1+p2+p3 = 1)

Let's suppose the response is as follows (Y1,Y2,Y3), where Yi = 0, if the respectively soda is favourite, and 1 otherwise.

Then, (Y1,Y2,Y3) ~ Multinomial(1,p1,p2,p3)

[The above can be a good model for the population]

We can carry out the usual estimations in the multinomial model.