Question

The following contingency table represents the voters’ opinion concerning a new tax

reform bill and their level of income.

Levels of Income

Opinion Low Medium High

For 213 203 182

Against 138 110 154

Apply chi-square (χ2

) test to examine whether the opinion of people on new tax bill is

independent from their income level. [Table value of chi- square (χ2

) at 5% level of

significance and for 2 degrees of freedom is 5.99]

Answer 1

$H_0:$ the opinion of people on new tax bill is independent from their income level

$H_a:$ ​the opinion of people on new tax bill is dependent from their income level

$\Chi^2=\sum \frac{(O_i-E_i)^2}{E_i}=7.878$

where

O_i is observation value,

E_i is expected value

E_i = row total * column total/ total

$df=(Rows-1)*(Columns-1) = (2-1)*(3-1) = 2$

critical value:

$\Chi^2_{crit}=5.99$

Since $\Chi^2>\Chi^2_{crit}$ we reject the null hypothesis. ​The opinion of people on new tax bill is dependent from their income level