Question

Based on the results of a survey questionnaire, 400 individuals were classified as either politically conservative, moderate, or liberal. In addition, each person was classified by age, as shown in the following table. Is there sufficient evidence to reject the hypothesis that "political preference is independent of age"? Use a.01. Age Group Older Than 50 Totals 68 211 121 400 20-35 14 80 36-50 35 90 21 146 19 Conservative Moderate Liberal Totals 56 138 116 (a) Find the test statistic. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer bounds exactly.) kp

Answer 1

Ho: political preference is indepedent of age

H1: political preference is not indepedent of age

Chi-Square Test
Observed Frequencies
	age group					Calculations
political preferance	20-35	36-50	older than 50	Total		fo-fe
conservative	14	35	19	68		-9.46	10.18	-0.72
moderate	80	90	41	211		7.205	12.985	-20.19
liberals	44	21	56	121		2.255	-23.165	20.91
Total	138	146	116	400
Expected Frequencies=Σrow*Σcolumn/Σ grandtotal
	age group
political preferance	20-35	36-50	older than 50	Total		(fo-fe)^2/fe
conservative	23.46	24.82	19.72	68		3.815	4.175	0.026
moderate	72.795	77.015	61.19	211		0.713	2.189	6.662
liberals	41.745	44.165	35.09	121		0.122	12.150	12.460
Total	138	146	116	400

a)

test stat=Σ(fo-fe)^2/fe = 42.31

df= (row-1)(column-1) = (3-1)(3-1) = 4

p value=0.0000 [excel fucntion: =chisq.dist.rt(42.31,4) ]

since, p value <α=0.01, reject Ho

so, there is enough evidence to reject the null hypothesis at α=0.01