Question

0	0.5	1.2	2	2.5	3	3.5	4	4.5	5.5
63	66	69	75	78	81	84	87	90	96

A survey asked students for their college and their satisfaction with their program. The results are provided in the tables below.

Determine if there is a relationship between college and satisfaction at the 0.05 level of significance.

H₀: College and Satisfaction are independent.

H_a: College and Satisfaction are dependent.

Determine the critical value from the chart. Explain what chart you used and how you found the value.

Determine the test statistic from your calculator. Explain what test you used in the calculator and the information you entered into the calculator.

Using your critical value and test statistic, state your conclusion. Explain how you arrived at your conclusion.

What is the conclusion in context?

Answer 1

df = (6-1)*(2-1)= 5

The critical value from the chart is 11.070.

The Chi-square test is used here.

The test statistic is 6.67.

Since 6.67 < 11.070, we fail to reject the null hypothesis.

Therefore, we can conclude that college and Satisfaction are independent.

		Col 1	Col 2	Total
Row 1	Observed	5	2	7
	Expected	4.11	2.89	7.00
	O - E	0.89	-0.89	0.00
	(O - E)² / E	0.19	0.28	0.47
Row 2	Observed	6	1	7
	Expected	4.11	2.89	7.00
	O - E	1.89	-1.89	0.00
	(O - E)² / E	0.87	1.24	2.11
Row 3	Observed	14	12	26
	Expected	15.25	10.75	26.00
	O - E	-1.25	1.25	0.00
	(O - E)² / E	0.10	0.15	0.25
Row 4	Observed	18	12	30
	Expected	17.60	12.40	30.00
	O - E	0.40	-0.40	0.00
	(O - E)² / E	0.01	0.01	0.02
Row 5	Observed	10	4	14
	Expected	8.21	5.79	14.00
	O - E	1.79	-1.79	0.00
	(O - E)² / E	0.39	0.55	0.94
Row 6	Observed	8	12	20
	Expected	11.73	8.27	20.00
	O - E	-3.73	3.73	0.00
	(O - E)² / E	1.19	1.68	2.87
Total	Observed	61	43	104
	Expected	61.00	43.00	104.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	2.76	3.91	6.67
		11.070	critical value
		6.67	chi-square
		5	df
		.2466	p-value