A national soccer team scores 1 goal per game on average. Let the data from the past 20 games be given by

1,2,2,1,1,1,1,2,1,4,0,2,3,0,2,1,0,3,4,1. 

Using this information, please answer the following questions.

(a) What is an appropriate statistical model for the number of goals scored in a given game if modeled by a random variable X taking values in {0, 1, 2, . . .}?

(b) Formulate an appropriate two-sided testing problem for the model’s parameter in (a).

(c) Use the likelihood ratio test statistic to test the null hypothesis in (b). (d) (2+3 points) Make a decision on the null hypothesis in (b) by means of