Answer
Step 1:
$H_0$ : Hospitals and Cesarean delivery rates are independent from each other.
$H_1$: Hospitals and Cesarean delivery rates are dependent upon each other.
Step 2:
Since α=0.1, the critical value using Table G with (2-1)(3-1) = (1)(2) =2 degrees of freedom is 4.605.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(111)(100)}{(300)}$ = 37
$E_1,2$ = $\frac{(111)(100)}{(300)}$ = 37
$E_1,3$ = $\frac{(111)(100)}{(300)}$= 37
$E_2,1$ = $\frac{(189)(100)}{(300)}$ = 63
$E_2,2$ = $\frac{(189)(100)}{(300)}$ = 63
$E_2,3$ = $\frac{(189)(100)}{(300)}$ = 63
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(44-37)^{2}}{37}$ + $\frac{(28-37)^{2}}{37}$ + $\frac{(39-37)^{2}}{37}$ + $\frac{(56-63)^{2}}{63}$ + $\frac{(72-63)^{2}}{63}$ + $\frac{(61-63)^{2}}{63}$
=1.324+2.189+0.108+0.778+1.286+0.063
=5.749
Step 4:
Since 5.749 > 4.605, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that hospitals and Cesarean delivery rates are dependent upon each other.
