Question

A basketball coach wanted to see if there was a relationship between a team and their training methods. 50 players were asked "Do you think practicing 5 times per week will help you win more games?" Below are each teams responses.  

Null hypothesis: A team and their training methods are independent.

Alternative hypothesis: A team and their training methods are dependent.  

Perform hypothesis testing using the Chi-Square Test for Independence and interpret the results.

Team	Strongly Agree	Agree	Neutral	Disagree	Strongly Disagree	Row Total
A	1	10	2	1	0	14
B	7	6	6	0	0	19
C	1	3	4	0	1	9
D	0	1	0	0	0	1
E	1	0	4	1	0	6
F	0	1	0	0	0	1
Column Total	10	21	16	2	1	50

Answer 1

Using excel<data<megastat<chi square<contigency

Chi-square Contingency Table Test for Independence
			Strongly Agree	Agree	Neutral	Disagree	Strongly Disagree	Total
	A	Observed	1	10	2	1	0	14
		Expected	2.80	5.88	4.48	0.56	0.28	14.00
		O - E	-1.80	4.12	-2.48	0.44	-0.28	0.00
		(O - E)² / E	1.16	2.89	1.37	0.35	0.28	6.04
	B	Observed	7	6	6	0	0	19
		Expected	3.80	7.98	6.08	0.76	0.38	19.00
		O - E	3.20	-1.98	-0.08	-0.76	-0.38	0.00
		(O - E)² / E	2.69	0.49	0.00	0.76	0.38	4.33
	C	Observed	1	3	4	0	1	9
		Expected	1.80	3.78	2.88	0.36	0.18	9.00
		O - E	-0.80	-0.78	1.12	-0.36	0.82	0.00
		(O - E)² / E	0.36	0.16	0.44	0.36	3.74	5.05
	D	Observed	0	1	0	0	0	1
		Expected	0.20	0.42	0.32	0.04	0.02	1.00
		O - E	-0.20	0.58	-0.32	-0.04	-0.02	0.00
		(O - E)² / E	0.20	0.80	0.32	0.04	0.02	1.38
	E	Observed	1	0	4	1	0	6
		Expected	1.20	2.52	1.92	0.24	0.12	6.00
		O - E	-0.20	-2.52	2.08	0.76	-0.12	0.00
		(O - E)² / E	0.03	2.52	2.25	2.41	0.12	7.33
	F	Observed	0	1	0	0	0	1
		Expected	0.20	0.42	0.32	0.04	0.02	1.00
		O - E	-0.20	0.58	-0.32	-0.04	-0.02	0.00
		(O - E)² / E	0.20	0.80	0.32	0.04	0.02	1.38
	Total	Observed	10	21	16	2	1	50
		Expected	10.00	21.00	16.00	2.00	1.00	50.00
		O - E	0.00	0.00	0.00	0.00	0.00	0.00
		(O - E)² / E	4.64	7.66	4.70	3.95	4.56	25.51
			25.51	chi-square
			20	df
			.1825	p-value

Answer:

Since P value= 0.1825

Let us assume the level of significance =0.05

Since p value>alpha(0.05). We fail to reject the null hypothesis.

There is mot sufficient evidence to conclude that a team and their training methods are dependent.