Answer
15.
Step 1:
$H_0$ : The program of study and type of institution are independent from each other.
$H_1$: The program of study and type of institution are dependent upon each other.
Step 2:
Since α=0.05, the critical value using Table G with (4-1)(2-1) = (3)(1) =3 degrees of freedom is 7.815.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(88)(302)}{(707)}$ = 37.59
$E_1,2$ = $\frac{(88)(405)}{(707)}$ = 50.41
$E_2,1$ = $\frac{(441)(302)}{(707)}$= 188.38
$E_2,2$ = $\frac{(441)(405)}{(707)}$ = 252.62
$E_3,1$ = $\frac{(87)(302)}{(707)}$ = 37.16
$E_3,2$ = $\frac{(87)(405)}{(707)}$ = 49.84
$E_4,1$ = $\frac{(91)(302)}{(707)}$ = 38.87
$E_4,2$ = $\frac{(91)(405)}{(707)}$ = 52.13
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(36-37.59)^{2}}{37.59}$ + $\frac{(52-50.41)^{2}}{50.41}$ + $\frac{(210-188.38)^{2}}{188.38}$ + $\frac{(231-252.62)^{2}}{252.62}$ + $\frac{(28-37.16)^{2}}{37.16}$ + $\frac{(59-49.84)^{2}}{49.84}$ + $\frac{(28-38.87)^{2}}{38.87}$ + $\frac{(63-52.13)^{2}}{52.13}$
=0.067+0.05+2.482+1.851+2.259+2.259+1.685+3.040+2.267
=13.702
Step 4:
Since 13.702 > 7.815, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the program of study and type of institution are dependent upon each other.
