Answer
$H_0$ : The hospitals and the proportions of those who were in the delivery room at the time of birth are independent from each other.
$H_1$: The hospitals and the proportions of those who were in the delivery room at the time of birth 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:
$E_1,1$ = $\frac{(239)(75)}{(300)}$ = 59.75
$E_1,2$ = $\frac{(239)(75)}{(300)}$ = 59.75
$E_1,3$ = $\frac{(239)(75)}{(300)}$= 59.75
$E_1,4$ = $\frac{(239)(75)}{(300)}$ = 59.75
$E_2,1$ = $\frac{(61)(75)}{(300)}$ = 15.25
$E_2,2$ = $\frac{(61)(75)}{(300)}$ = 15.25
$E_2,3$ = $\frac{(61)(75)}{(300)}$ = 15.25
$E_2,4$ = $\frac{(61)(75)}{(300)}$ = 15.25
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(66-59.75)^{2}}{59.75}$ + $\frac{(60-59.75)^{2}}{59.75}$ + $\frac{(57-59.75)^{2}}{59.75}$ + $\frac{(56-59.75)^{2}}{59.75}$ + $\frac{(9-15.25)^{2}}{15.25}$ + $\frac{(15-15.25)^{2}}{15.25}$ + $\frac{(18-15.25)^{2}}{15.25}$ + $\frac{(19-15.25)^{2}}{15.25}$
=0.654+0.001+0.127+0.235+2.561+0.004+0.496+0.922
=5.000
Step 4:
Since 5 < 7.815, the decision is to not reject the null hypothesis.
Step 5:
There is not enough evidence to claim that the hospitals and the proportions of those who were in the delivery room at the time of birth are dependent upon each other.
