Answer
Step 1:
$H_0$ :The length of unemployment is independent from the type of industry.
$H_1$: The length of unemployment is dependent upon the type of industry.
Step 2:
Since α=0.05, the critical value using Table G with (3-1)(3-1) = (2)(2) =4 degrees of freedom is 9.488.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(275)(216)}{(733)}$ = 81.04
$E_1,2$ = $\frac{(275)(278)}{(733)}$ = 104.30
$E_1,3$ = $\frac{(275)(239)}{(733)}$= 89.67
$E_2,1$ = $\frac{(150)(216)}{(733)}$ = 44.20
$E_2,2$ = $\frac{(150)(278)}{(733)}$ = 56.89
$E_2,3$ = $\frac{(150)(239)}{(733)}$ = 48.91
$E_3,1$ = $\frac{(308)(216)}{(733)}$ = 90.76
$E_3,2$ = $\frac{(308)(278)}{(733)}$ = 116.81
$E_3,3$ = $\frac{(308)(239)}{(733)}$ = 100.43
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(85-81.04)^{2}}{81.04}$ + $\frac{(110-104.30)^{2}}{104.30}$ + $\frac{(80-89.67)^{2}}{89.67}$ + $\frac{(48-44.20)^{2}}{44.20}$ + $\frac{(57-56.89)^{2}}{56.89}$ + $\frac{(45-48.91)^{2}}{48.91}$ + $\frac{(83-90.76)^{2}}{90.76}$ + $\frac{(111-116.81)^{2}}{116.81}$ + $\frac{(114-100.43)^{2}}{100.43}$
=0.194+0.312+1.042+0.326+0+0.312+0.664+0.289+1.835
=4.974
Step 4:
Since 4.974 < 9.488, the decision is not to reject the null hypothesis.
Step 5:
There is not enough evidence to claim that the length of unemployment is dependent upon the type of industry.
