Answer
$H_0$ : The type of jobs and the years (10 years ago or now) are independent from each other.
$H_1$: The type of jobs and the years (10 years ago or now) 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:
$E_1,1$ = $\frac{(59)(25)}{(100)}$ = 14.75
$E_1,2$ = $\frac{(59)(25)}{(100)}$ = 14.75
$E_1,3$ = $\frac{(59)(25)}{(100)}$= 14.75
$E_1,4$ = $\frac{(59)(25)}{(100)}$= 14.75
$E_2,1$ = $\frac{(41)(25)}{(100)}$ = 10.25
$E_2,2$ = $\frac{(41)(25)}{(100)}$ = 10.25
$E_2,3$ = $\frac{(41)(25)}{(100)}$ = 10.25
$E_2,4$ = $\frac{(41)(25)}{(100)}$ = 10.25
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(14-14.75)^{2}}{14.75)}$ + $\frac{(13-14.75))^{2}}{14.75)}$ + $\frac{(17-14.75))^{2}}{14.75)}$ + $\frac{(15-14.75))^{2}}{14.75)}$ + $\frac{(11-10.25)^{2}}{10.25}$ + $\frac{(12-10.25)^{2}}{10.25}$ + $\frac{(8-10.25)^{2}}{10.25}$ + $\frac{(10-10.25)^{2}}{10.25}$
=0.038+0.208+0.343+0.004+0.056+0.299+0.494+0.006
=1.447
Step 4:
Since 1.447< 7.815, the decision is to not reject the null hypothesis.
Step 5:
There is not enough evidence to claim that the type of jobs and the years (10 years ago or now) are dependent upon each other.
