assignment 1

3.docx

Home >Foreign Languages homework help >Spanish homework help >assignment 1

The number of goals per game scored by teams in a professional soccer league are shown below for a sample of 180 games:

# of Goals	0	1	2	3	4	5
# of Games	57	53	41	19	8	2

We would like to conduct a chi-square goodness of fit test at the 5% level of significance to determine whether the number of goals scored per game by teams in the league has a Poisson distribution. Since a Poisson variable can take any non-negative integer value, it is possible that the number of goals is even greater than 5 (even though there are no games in this sample for which X > 5). As such, we must label the last column "".

# of Goals	0	1	2	3	4
# of Games	57	53	41	19	8	2
Expected Count

(a) Since we don't know the value of the parameter , we must estimate it. The estimated value of is . (b) Enter the expected cell counts in the table above. (When you are calculating probabilities for the Poisson distribution, round your probabilities to four decimal places. Then round your expected cell counts to two decimal places.) Since the last cell has an expected count less than 5, we must merge it with the cell to its left. We will label this new cell "". Our final merged table is shown below:

# of Goals	0	1	2	3
# of Games	57	53	41	19	10
Expected
Cell Chi-Square

(d) The value of the test statistic for the appropriate test of significance (rounded to two decimal places) is . (e) The P-value for the appropriate test of significance is between and . (f) If we used the critical value method to conduct the test, the decision rule would be to reject H0 if . (g) What is the correct conclusion for this test?

Fail to reject H0. There is insufficient evidence that the number of goals per game by a team does not have a Poisson distribution.

Reject H0. There is insufficient evidence that the number of goals per game by a team does not have a Poisson distribution.

Fail to reject H0. There is sufficient evidence that the number of goals per game by a team does not have a Poisson distribution.

Reject H0. There is insufficient evidence that the number of goals per game by a team has a Poisson distribution.

Fail to reject H0. There is insufficient evidence that the number of goals per game by a team has a Poisson distribution.

Reject H0. There is sufficient evidence that the number of goals per game by a team has a Poisson distribution.

Reject H0. There is sufficient evidence that the number of goals per game by a team does not have a Poisson distribution.

Fail to reject H0. There is sufficient evidence that the number of goals per game by a team has a Poisson distribution.