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 Al A Little 30 29 26 59 Extremely Somewhat Very 13 24 25 78 28 Age 20-29 Age 30-39 Age 40-49 Age 50 or older 16 49 20 120 Carry out a chi-square test. Test Ho 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 a0.01 χ2 (40,0001)-l- P (0.0001) - O There is no a relationship between age and how politically informed the person is O There is a relationship between age and how politically informed the person is

Answer 1

Answer Date: 26/04/2019 Test the claim that there is a relationship between age and how politically informed the person is at 1% level of significance. The null and alternative hypothesis is, The null hypothesis is that there is no relationship between age and how politically informed the person is s The altemative hypothesis is that there is a relationship between age and how politically informed the person is The chi-square statistics is, By using Excel software, find chi-square test statistics with the help of following steps: 1) Import the data. 2) Select Contingency table from Chi-Square in MegaStat option from Add-Ins menu 3) Select Chi-Square and Expected frequencies in Output options 4)Click Ok.

Chi-square Contingency Table Test for Independence A little Somewhat 28 31.40 Total 78 78.00 134 134.00 115 115.00 299 299.00 626 626.00 Not at all Very Extreme Age 20-29 Observed Expected Age 30-39 Observed Expected Age 40-49 Observed Expected Age 50 or older Observed Expected Observed Expected 13 17.44 24 29.97 25 25.72 78 66.87 140 140.00 30 17.94 29 30.82 26 26.45 59 68.78 144 144.00 5.61 16 9.63 5.61 10 9.63 13 8.27 53.94 49 46.29 120 120.36 252 252.00 8.27 20 21.49 45 45.00 21.49 45 45.00 Total 32.1033 chi-square 12 df 0013 p-value From the Excel output, the chi-square test statistic is 32.1033 Thep-value is, From the Excel output, the chi-square testp-value is 0.0013 The p-value is 0.0013

Decision The conclusion is that the signiicant p-value is less than 0.01 which is 0.0013, so the null hypothesis is rejected at 1% level of significance. There is sufficient evidence to indicate that there is a relationship between age and how politically informed the person is. The result is statistically significant The answer option is 2