A researcher is studying the determinants of statefinanced w

A researcher is studying the determinants of state-financed welfare programs in the United States such as unemployment compensation and aid to dependent children. She feels that because states in which the average income is high have larger tax revenues, they are better able to afford welfare programs. Therefore, she hypothesizes that the higher the average income in a state, the more welfare programs the state legislature will have adopted. She obtains data pertaining to the average income of the residents of each state (coded low; high) and the number of welfare programs passed by each state legislature (coded few: many). These data yield the following cross-tabulation: Average Income Loy Average Number of Welfare Programs Few Many High 16 14

Solution

here we go for the chi-square test for independence of attributes i.e. high average income and passage of welfare program are independent

total chi-squre =0.3333 and p-vavlue for this chi-square at 1 df=0.563

so at (let) alpha=0.05 which is less than p-value.

conclusion at alpha=0.05 ,high average income in state does not lead to passage of welfare program are independent

O	E	O-E	(O-E)2	chi-square
9	10	-1	1	0.1
16	15	1	1	0.066667
11	10	1	1	0.1
14	15	-1	1	0.066667
			total chi-sq=	0.333333