Answer
Step 1:
$H_0$ : The proportions of volunteers and the age groups are independent from each other.
$H_1$: The proportions of volunteers and the age groups are dependent upon each other.
Step 2:
Since α=0.05, the critical value using Table G with (2-1)(5-1) = (1)(4) =4 degrees of freedom is 9.488.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(104)(19)}{(375)}$ = 20.80
$E_1,2$ = $\frac{(104)(18)}{(375)}$ = 20.80
$E_1,3$ = $\frac{(104)(23)}{(375)}$= 20.80
$E_1,4$ = $\frac{(104)(31)}{(375)}$= 20.80
$E_1,5$ = $\frac{(104)(13)}{(375)}$=20.80
$E_2,1$ = $\frac{(271)(56)}{(375)}$ =54.20
$E_2,2$ = $\frac{(271)(57)}{(375)}$ = 54.20
$E_2,3$ = $\frac{(271)(52)}{(375)}$ = 54.20
$E_2,4$ = $\frac{(271)(44)}{(375)}$ = 54.20
$E_2,5$ = $\frac{(271)(62)}{(375)}$ = 54.20
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(19-20.80)^{2}}{20.80}$ + $\frac{(18-20.80)^{2}}{20.80}$ + $\frac{(23-20.80)^{2}}{20.80}$ + $\frac{(31-20.80)^{2}}{20.80}$ + $\frac{(33-320.80)^{2}}{20.80}$ + $\frac{(56-54.20)^{2}}{54.20}$ + $\frac{(57-54.20)^{2}}{54.20}$ + $\frac{(52-54.20)^{2}}{54.20}$ + $\frac{(44-54.20)^{2}}{54.20}$ + $\frac{(62-54.20)^{2}}{54.20}$
=0.156+0.37+0.233+5.002+2.925+0.060+0.145+0.089+1.920+1.123
=12.028
Step 4:
Since 12.028 > 9.488, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the proportions of volunteers and the age groups are dependent upon each other.
