Question

In 2012, the General Social Survey asked a random sample of adults, "Compared to most people, how informed are you about politics?" Suppose that the following are the data classified by their responses to this question and their age group (the data has been modified slightly for testing purposes):

	Not at All	A little	Somewhat	Very	Extremely
Age 20-29	7	29	28	13	0
Age 30-39	16	29	56	22	8
Age 40-49	3	24	50	26	14
Age 50 or Older	20	60	121	80	23

Carry out a chi-square test. Test H0: there is no relationship between age and how politically informed the person is versus Ha: there is a relationship between age and how politically informed the person is. Use α=0.01. χ2(±0.0001)= ______

P(±0.0001)= _______

a) There is no a relationship between age and how politically informed the person is

b) There is a relationship between age and how politically informed the person is

Answer 1

Ans:

	Observed(fo)
	Not at All	A little	Somewhat	Very	Extremely	Total
Age 20-29	7	29	28	13	0	77
Age 30-39	16	29	56	22	8	131
Age 40-49	3	24	50	26	14	117
Age 50 or Older	20	60	121	80	23	304
Total	46	142	255	141	45	629
	Expected(fe)
	Not at All	A little	Somewhat	Very	Extremely	Total
Age 20-29	5.63	17.38	31.22	17.26	5.51	77
Age 30-39	9.58	29.57	53.11	29.37	9.37	131
Age 40-49	8.56	26.41	47.43	26.23	8.37	117
Age 50 or Older	22.23	68.63	123.24	68.15	21.75	304
Total	46	142	255	141	45	629
	Chi square=(fo-fe)^2/fe
	Not at All	A little	Somewhat	Very	Extremely	Total
Age 20-29	0.3327	7.7633	0.3314	1.0517	5.5087	14.9879
Age 30-39	4.3018	0.0111	0.1575	1.8475	0.2009	6.5188
Age 40-49	3.6083	0.2205	0.1390	0.0020	3.7862	7.7559
Age 50 or Older	0.2241	1.0851	0.0408	2.0619	0.0720	3.4839
Total	8.4670	9.0801	0.6687	4.9631	9.5678	32.7466

Test statistic:

Chi square=32.7466

df=(4-1)*(5-1)=3*4=12

p-value=CHIDIST(32.7466,12)=0.0011

As,p-value<0.01,we reject the null hypothesis.

Option b is correct.

There is a relationship between age and how politically informed the person is