Question

16. What's in a Word? Part II In a recent survey conducted by the Pew Research Center, a random sample of adults 18 years of age or older living in the continental United States was asked their reaction to the word capitalism. In addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table on the next page.

Answer 1

(a)

H0: Political affiliation and reaction to the word capitalism are independent.

H1: Political affiliation and reaction to the word capitalism are not independent but related to each other.

Democrat Independent RepublicanTOTA Chi-square calculation Observed. o Expected E YO-E)2/E 235 265.157572 3.429957 264 233.842428 3.889282 288 294.383356 0.138416 66 259.616644 0.156952 25600779 2 Positive 235 3 Negative264 4 TOTAL499 288 26600 1571111 687 554 W、m413, 1466 7 Democrat Independent Republican 256 219.459072 6.08423 8 Positive 265.1576 294.388356 219.45907 9 Negative 233.8424259.616644 193.54093 10 TOTAL499 687 1466 157 193.540928 6.899003 20.59784 554 413 12

Expected frequency =row total*Column total/N

(where N =overall total =1466)

The test statistic, Chi-square value =$\chi^2$ =20.598

Critical value of Chi-square at 0.05 significance level and at df =(r-1)(c-1) =(2-1)(3-1) =2 is $\chi^2(critical)$ =5.991

Conclusion: Since $\chi^2 > \chi^2(critical)$ ​​​​​​, we reject the null hypothesis(H0) at 5% significance level and so, there is a strong statistical evidence to claim that there is a relationship between the two variables - reaction to the word capitalism and political affiliation. Thus, the evidence suggests that individuals within each political affiliation react differently to the word capitalism.

(b)

Conditional distribution of reaction by political party:

	Democrat	Independent	Republican	Total
Positive	235/499 =0.47	288/554 =0.52	256/413 =0.62	779
Negative	264/499 =0.53	266/554 =0.48	157/413 =0.38	687
Total	499	554	413	1466

(c)

Among Democrats and Independents, the reaction to the word capitalism is almost equal for positive and negative reactions whereas among Republicans, positive reaction to the word capitalism is more than that of negative reaction. So, it seems "partisan divide" applies more to the Republicans than the Democrats and Independents.