Answer
Step 1:
$H_0$ : The proportions of students favoring foreign language-speaking dorms and the class are independent from each other.
$H_1$: The proportions of students favoring foreign language-speaking dorms and the class are dependent upon each other.
Step 2:
Since α=0.05, the critical value using Table G with (2-1)(4-1) = (1)(3) =3 degrees of freedom is 7.815.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(67)(50)}{(200)}$ = 16.75
$E_1,2$ = $\frac{(67)(50)}{(200)}$ = 16.75
$E_1,3$ = $\frac{(67)(50)}{(200)}$= 16.75
$E_1,4$ = $\frac{(67)(50)}{(200)}$ = 16.75
$E_2,1$ = $\frac{(133)(50)}{(200)}$ = 33.25
$E_2,2$ = $\frac{(133)(50)}{(200)}$ = 33.25
$E_2,3$ = $\frac{(133)(50)}{(200)}$ = 33.25
$E_2,4$ = $\frac{(133)(50)}{(200)}$ = 33.25
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(10-16.75)^{2}}{16.75}$ + $\frac{(15-16.75)^{2}}{16.75}$ + $\frac{(20-16.75)^{2}}{16.75}$ + $\frac{(22-175)^{2}}{16.75}$ + $\frac{(40-33.25)^{2}}{33.25}$ + $\frac{(35-33.25)^{2}}{33.25}$ + $\frac{(30-33.25)^{2}}{33.25}$ + $\frac{(28-33.25)^{2}}{33.25}$
=2.720+0.183+0.631+1.646+1.370+0.092+0.318+0.829
=7.788
Step 4:
Since 7.788 < 7.815, the decision is not to reject the null hypothesis.
Step 5:
There is no enough evidence to claim that the proportions of students favoring foreign language-speaking dorms and the class are dependent upon each other.
