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In 2012, the General Social Survey asked a random sample of adults, \"Compared to most people,...

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Basic Math

In 2012, the General Social Survey asked a random sample ofadults, \"Compared to most people, how informed are you aboutpolitics?\" Suppose that the following are the data classified bytheir responses to this question and their age group (the data hasbeen modified slightly for testing purposes):

Not at AllA littleSomewhatVeryExtremely
Age 20-2972928130
Age 30-39162956228
Age 40-49324502614
Age 50 or Older20601218023

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

P(±0.0001)= _______

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

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

Answer & Explanation Solved by verified expert
3.7 Ratings (301 Votes)

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
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