Answer
$H_0$ : The proportions of the students who prefer that their mothers have jobs outside the home and school levels of the students are independent from each other.
$H_1$: The proportions of the students who prefer that their mothers have jobs outside the home and school levels of the students are dependent upon each other.
Step 2:
Since α=0.10, the critical value using Table G with (2-1)(3-1) = (1)(2) =2 degrees of freedom is 4.605.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(118)(60)}{(180)}$ = 39.33
$E_1,2$ = $\frac{(118)(60)}{(180)}$ = 39.33
$E_1,3$ = $\frac{(118)(60)}{(180)}$= 39.33
$E_2,1$ = $\frac{(62)(60)}{(180)}$ = 20.67
$E_2,2$ = $\frac{(62)(60)}{(180)}$ = 20.67
$E_2,3$ = $\frac{(62)(60)}{(180)}$ = 20.67
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(29-39.33)^{2}}{39.33}$ + $\frac{(38-39.33)^{2}}{39.33}$ + $\frac{(51-39.33)^{2}}{39.33}$ + $\frac{(31-20.67)^{2}}{20.67}$ + $\frac{(22-20.67)^{2}}{20.67}$ + $\frac{(9-20.67)^{2}}{20.67}$
=2.715+0.045+3.460+5.167+0.086+6.586
=18.059
Step 4:
Since 18.059 > 4.605 , the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the proportions of the students who prefer that their mothers have jobs outside the home and school levels of the students are dependent upon each other.
