Answer
Step 1:
$H_0$ : The year and type of transplant are independent from each other.
$H_1$: The program of study and type of transplant are dependent upon each other.
Step 2:
Since α=0.01, the critical value using Table G with (3-1)(3-1) = (2)(2) =4 degrees of freedom is 13.277.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(3006)(4155)}{(9469)}$ = 1319.03
$E_1,2$ = $\frac{(3006)(2653)}{(9469)}$ = 842.21
$E_1,3$ = $\frac{(3006)(2661)}{(9469)}$= 844.75
$E_2,1$ = $\frac{(4069)(4155)}{(9469)}$ = 1785.48
$E_2,2$ = $\frac{(4069)(2653)}{(9469)}$ = 1140.04
$E_2,3$ = $\frac{(4069)(2661)}{(9469)}$ = 1143.48
$E_3,1$ = $\frac{(2394)(4155)}{(9469)}$ = 1050.49
$E_3,2$ = $\frac{(2394)(2653)}{(9469)}$ = 670.74
$E_3,3$ = $\frac{(2394)(2661)}{(9469)}$ = 672.77
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(2056-1319.03)^{2}}{1319.03}$ + $\frac{(870-842.21)^{2}}{842.21}$ + $\frac{(80-844.75)^{2}}{844.75}$ + $\frac{(2016-1785.48)^{2}}{1785.48}$ + $\frac{(880-1140.04)^{2}}{1140.04}$ + $\frac{(1173-1143.48)^{2}}{1143.48}$ + $\frac{(83-1050.49)^{2}}{1050.49}$ + $\frac{(903-670.74)^{2}}{670.74}$ + $\frac{(1408-672.77)^{2}}{672.77}$
=411.755+0.917+692.329+29.762+59.315+.762+891.046+80.422+803.498
=2969.807
Step 4:
Since 2969.807 > 13.277, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the program of study and type of transplant are dependent upon each other.
