Question

I need a step by step answer for the following question:

Four states were randomly selected, and their members in the U.S. House of Representatives (114th Congress) are noted. At a = 0.10, can it be concluded that there is a dependent relationship between the state and the political party affiliation of its representatives?

	California	Florida	Illinois	Texas
Democrat	39	10	10	11
Republican	14	17	8	25

Answer 1

Ans:

Chi square test for goodness of fit:

H₀:There is a Independent relationship between the state and the political party affiliation.

H_a:There is a dependent relationship between the state and the political party affiliation.

Expected count(fe)=row sum*column sum/overall sum

	Observed(fo)
	California	Florida	Illinois	Texas	Total
Democrat	39	10	10	11	70
Republican	14	17	8	25	64
Total	53	27	18	36	134
	Expected(fe)
	California	Florida	Illinois	Texas	Total
Democrat	27.69	14.10	9.40	18.81	70
Republican	25.31	12.90	8.60	17.19	64
Total	53	27	18	36	134
	Chi square=(fo-fe)^2/fe
	California	Florida	Illinois	Texas	Total
Democrat	4.623	1.194	0.038	3.240	9.095
Republican	5.056	1.306	0.041	3.544	9.948
Total	9.679	2.501	0.079	6.784	19.043

Test statistic:

Chi square=19.043

number of rows,r=2

number of columns,c=4

df=(2-1)*(4-1)=3

p-value=CHIDIST(19.043,3)=0.0003

As,p-value<0.10,we reject the null hypothesis.

There is sufficient evidence to conclude that there is a dependent relationship between the state and the political party affiliation.