Question

Do people think that diversity in a large population is healthy or damaging? At one college, responses of a randomly selected group of students found that 10 students majoring in behavioral sciences thought diversity healthy and 3 thought it damaging. In the natural sciences, 4 thought diversity healthy and 8 thought it damaging. In the arts, 18 thought diversity healthy and 7 thought it damaging. In the languages, 6 thought diversity healthy and 7 thought it damaging. Finally, in the field of history, 4 students thought diversity healthy and 9 thought it damaging. Do these results suggest that opinions about diversity vary over different majors? (Use the .05 significance level.)

Choose the appropriate test and use the five steps of hypothesis testing!   

Answer 1

The hypothesis being tested is:

H0: Opinions about diversity does not vary over different majors

Ha: Opinions about diversity vary over different majors

		Healthy	Damaging	Total
Behavioral science	Observed	10	3	13
	Expected	7.18	5.82	13.00
	O - E	2.82	-2.82	0.00
	(O - E)² / E	1.10	1.36	2.47
Natural sciences	Observed	4	8	12
	Expected	6.63	5.37	12.00
	O - E	-2.63	2.63	0.00
	(O - E)² / E	1.04	1.29	2.33
Arts	Observed	18	7	25
	Expected	13.82	11.18	25.00
	O - E	4.18	-4.18	0.00
	(O - E)² / E	1.27	1.57	2.83
Languages	Observed	6	7	13
	Expected	7.18	5.82	13.00
	O - E	-1.18	1.18	0.00
	(O - E)² / E	0.20	0.24	0.44
History	Observed	4	9	13
	Expected	7.18	5.82	13.00
	O - E	-3.18	3.18	0.00
	(O - E)² / E	1.41	1.74	3.15
Total	Observed	42	34	76
	Expected	42.00	34.00	76.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	5.02	6.20	11.22
		11.22	chi-square
		4	df
		.0242	p-value

The p-value is 0.0242.

Since the p-value (0.0242) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that opinions about diversity vary over different majors.