We take a random sample of size n = 100 from the population of students at the a campus and ask them about their soft drink preferences, with "Diet Coke", "Dr Pepper" and "Mountain Dew" as possible choices. Our goal is to determine the proportion p1 of students who like Diet Coke, the proportion p2 of students who like Dr Pepper and the proportion p3 of those who like Mountain Dew.

The observed data has the following distribution (numbers give us the number of students who prefer the corresponding soft drink) Diet Coke Dr Pepper (a) (2 marks) What is an appropriate statistical model for this experiment? Justify your answer for full credit. (b) (3 marks] Based on the model chosen in (a) and the observed data, use an appropriate Likelihood ratio test to check the hypothesis Hi3 :p1 = 1/4: p2 = 1/21 P3 = 1/4" Show all your work for full credit