Answer
Step 1:
$H_0$ : The study groups and the professors are independent from each other.
$H_1$: The study groups and the professors are dependent upon each other.
Step 2:
Since α=0.05, the critical value using Table G with (3-1)(3-1) = (2)(2) =4 degrees of freedom is 9.488.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(62)(58)}{(174)}$ = 20.67
$E_1,2$ = $\frac{(62)(55)}{(174)}$ = 19.60
$E_1,3$ = $\frac{(62)(61)}{(174)}$= 21.74
$E_2,1$ = $\frac{(55)(58)}{(174)}$ = 18.33
$E_2,2$ = $\frac{(55)(55)}{(174)}$ = 17.39
$E_2,3$ = $\frac{(55)(61)}{(174)}$ = 19.28
$E_3,1$ = $\frac{(57)(58)}{(174)}$ = 19
$E_3,2$ = $\frac{(57)(55)}{(174)}$ = 18.02
$E_3,3$ = $\frac{(57)(61)}{(174)}$ = 19.98
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(25-20.67)^{2}}{20.67}$ + $\frac{(22-19.60)^{2}}{19.60}$ + $\frac{(15-21.74)^{2}}{21.74}$ + $\frac{(16-18.33)^{2}}{18.33}$ + $\frac{(16-18.33)^{2}}{18.33}$ + $\frac{(15-17.39)^{2}}{17.39}$ + $\frac{(24-19.28)^{2}}{19.28}$ + $\frac{(17-19)^{2}}{19}$ + $\frac{(18-18.02)^{2}}{18.02}$ + $\frac{(22-19.98)^{2}}{19.98}$
=0.909+0.294+2.087+0.297+0.327+1.155+0.211+0+0.204
=5.483
Step 4:
Since 5.483 < 9.488, the decision is not to reject the null hypothesis.
Step 5:
There is not enough evidence to claim that the study groups and the professors are dependent upon each other.
