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 average income is high have larger tax revenues, they are better to 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 permitting 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; many). These data tied the following cross-tabulation.

  Average Income

Number of Welfare Programs Low High

Few 9 16

Many 11 14

In reporting her results of her study, the researcher comments about the above cross-tabulation: \"Because more states in which the average income is high (14) have passed many welfare programs that have states in which the average income is low (11), this table provides support for the hypothesis. High average income in a state tends to lead to the passage of welfare programs.\" Do you agree with the conclusion reached by this researcher? Present evidence to support your answer.

Solution

here we go for chi-squre test for independency of attributes

Ho: there is no relationship between average income and welfare program

Ha: there is dependency between average income and welfare program

  Average Income

Number of Welfare Programs Low High total

Few 9 16 25

Many 11 14 25

20 30 50

E(9)=25x20/50, E(16)=25x30/50,E(11)=20x25/50, E(14)=30x25/50

chi-square statistic=(O-E)²/E with df=1

here O are 9,16,11,14 and

E are 10,15,10,15

chi-squre=0.3333

P=0.5637

since P is more than 0.05 so we say that at 5% level of significance we reject alternative hypothesis and accept null hypothesis that  there is no relationship between average income and welfare program.

conclusion:High average income in a state does not tend to lead to the passage of welfare programs.\"