Question

Hockey Teams: There are five teams in the northeast conference of the NHL. Their win/loss records for the 2010/2011 season are summarized in the table below.

Observed Frequencies: O_i's

	Montreal	Boston	Toronto	Ottawa	Buffalo
	Canadiens	Bruins	Maple Leafs	Senators	Sabres	Totals
Wins	44	46	37	32	43	202
Losses	38	36	45	50	39	208
Totals	82	82	82	82	82	410

The Test: Test for a significant dependent relationship between wins/losses and team for this season. Conduct this test at the 0.05 significance level.

(a) What is the null hypothesis for this test?

H₀: The win/loss record of a team in the northeast conference is significantly dependent of which team it is.H₀: The win/loss record of a team in the northeast conference is independent of which team it is.     

(b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places.

χ²

=

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven that win/loss record of the team is independent of which team it is.The evidence suggests that the win/loss record of the team is significantly dependent on which team it is.    There is not enough evidence to conclude that the win/loss record of the team is significantly dependent on which team it is.

Answer 1

Expected	Canadians	Bruins	Maple Leafs	Senators	Sabres
Wins	82*202/410=40.4	82*202/410=40.4	82*202/410=40.4	82*202/410=40.4	82*202/410=40.4
Losses	82*208/410=41.6	82*208/410=41.6	82*208/410=41.6	82*208/410=41.6	82*208/410=41.6

SD	Canadians	Bruins	Maple Leafs	Senators	Sabres
Wins	(40.4-44)^2/40.4=0.321	(40.4-46)^2/40.4=0.776	(40.4-37)^2/40.4=0.286	(40.4-32)^2/40.4=1.747	(40.4-43)^2/40.4=0.167
Losses	(41.6-38)^2/41.6=0.312	(41.6-36)^2/41.6=0.754	(41.6-45)^2/41.6=0.278	(41.6-50)^2/41.6=1.696	(41.6-39)^2/41.6=0.163

Test Statistic
The Chi-square test statistic is computed as follows
χ^2 = 0.321 + 0.776 + 0.286 + 1.747 + 0.167 + 0.312 + 0.754 + 0.278 + 1.696 + 0.163
χ^2 = 6.500

c)
The corresponding p-value of the test is p = P(χ^2 > 6.5) = 0.1648

d)
Fail to reject H0

e)
There is not enough evidence to conclude that the win/loss record of the team is significantly dependent on which team it is.