Question

Question 3:

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) (1 point) 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) (1 point) Formulate an appropriate two-sided testing problem for the model’s parameter in (a).

(c) (3 points) 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

- an appropriate confidence interval - an appropriate p-value.

Answer 1

a) The poisson distribution is used for the count data an appropriate 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) The two side testing problem for the models patameter in a) is that

U1= consider the average score of 1 goal per game

U2= Actual average score of 1 goal per game from data

Ho: U1=U2 (U1 is equal to U2)  vs H1: U1 is not equal to U2

c) The likelihood ratio test statistic is given below

The p-value =0.109 and alpha=0.05

P-value is greater than alpha i.e(p-value>alpha) then accept Ho (null hypothesis)

Then it is conclude that the mean difference of consider one goal average per game is may be equal to the actual

average of the real data at 5% of level of significance.