Question

2. Your friend notices that the data for Q1 should control for player position. The updated data are provided below. (Note that as one player per position was selected, data are not meant to be identical to that from Q1 – the inconsistency is not an error).

	Team
Position	Bruins	Habs	Maple Leafs	Lightning	Panthers
Right wing	48	22	31	33	25
Center	31	17	47	29	20
Left wing	28	22	21	26	29
Defense	9	15	5	11	5

2a. State the null and alternative hypotheses (1 point)

2b. Calculate the test statistic (3 points) and state your conclusion using an alpha of 5% (1 point)

2c. Which position(s) is/are significantly different from one another? (2 points)

Answer 1

Answer;

Given that:

Your friend notices that the data for Q1 should control for player position. The updated data are provided below.

Position	Bruins	Habs	Maple Leafs	Lighting	Panthers
Right wing	48	22	31	33	25
Center	31	17	47	29	20
Left wing	28	22	21	26	29
Defense	9	15	5	11	5

The hypothesis being tested is

: There is no significant difference between team and position

: There is a significant difference between team and position

		Col 1	Col 2	Col 3	Col 4	Col 5	Total
Row 1	Observed	48	22	31	33	25	159
	Expected	38.91	25.49	34.89	26.50	26.50	159.00
	O-E	9.09	-3.49	-3.89	-1.50	-1.50	0.00
	(O-E)^2/E	2.12	0.48	0.43	0.08	0.08	3.12
Row 2	Observed	31	17	47	29	20	144
	Expected	35.24	23.09	31.59	30.08	24.00	144.00
	O-E	-4.24	-6.09	15.41	-1.08	-4.00	0.00
	(O-E)^2/E	0.51	1.61	7.51	0.04	0.67	10.33
Row 3	Observed	28	22	21	26	29	126
	Expected	30.84	20.20	27.65	26.32	21.00	126.00
	O-E	-2.84	1.80	-6.65	-0.32	8.00	0.00
	(O-E)^2/E	0.26	0.16	1.60	0.00	3.05	5.07
Row 4	Observed	9	15	5	11	5	45
	Expected	11.01	7.22	9.87	9.40	7.50	45.00
	O-E	-2.01	7.78	-4.87	1.60	-2.50	0.00
	(O-E)^2/E	0.37	8.40	2.41	0.27	0.83	12.28
Total	Observed	116	76	104	99	79	474
	Expected	116.00	76.00	104.00	99.00	79.00	474.00
	O-E	0.00	0.00	0.00	0.00	0.00	0.00
	(O-E)^2/E	3.26	10.64	11.95	0.32	4.63	30.80

Chi square = 30.80

df = 12

p-value = 0.0021

The test statistic is 30.80

The p-value is 0.0021

Since the p-value (0.0021) is less than the significance level(0.05).We can reject the null hypothesis

Therefore we can conclude that there is significance difference between team and position