Answer
14.
Step 1:
$H_0$ : The state and the political party affiliation are independent from each other.
$H_1$: The state and the political party affiliation are dependent upon each other.
Step 2:
Since α=0.05, the critical value using Table G with (4-1)(2-1) = (3)(1) =3 degrees of freedom is 7.815.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(72)(53)}{(134)}$ = 28.48
$E_1,2$ = $\frac{(72)(27)}{(134)}$ = 14.51
$E_1,3$ = $\frac{(72)(18)}{(134)}$= 9.67
$E_1,4$ = $\frac{(72)(36)}{(134)}$ = 19.34
$E_2,1$ = $\frac{(62)(53)}{(134)}$ = 24.52
$E_2,2$ = $\frac{(62)(27)}{(134)}$ = 12.49
$E_2,3$ = $\frac{(62)(18)}{(134)}$ = 8.33
$E_2,4$ = $\frac{(62)(36)}{(134)}$ = 16.66
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(38-28.48)^{2}}{28.48}$ + $\frac{(10-14.51)^{2}}{14.51}$ + $\frac{(12-9.67)^{2}}{9.67}$ + $\frac{(12-19.34)^{2}}{19.34}$ + $\frac{(15-24.52)^{2}}{24.52}$ + $\frac{(17-12.49)^{2}}{12.49}$ + $\frac{(6-8.33)^{2}}{8.33}$ + $\frac{(24-16.66)^{2}}{16.66}$
=3.184+1.4+0.561+2.788+3.698+1.626+0.651+3.237
=17.145
Step 4:
Since 17.145 > 7.815, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the state and the political party affiliation are dependent upon each other.
