Answer
$X^2\lt X_α^2$: the null hypothesis is not rejected.
There is no significant difference among the groups in attendance patterns.
Remember: we are studying people. People have emotions which make their behavior unpredictable. They can skip class for many reasons. We can not say, from these results, that the location of a student's seat in a classroom plays a role in attendance.
Work Step by Step
$H_0:$ the attendance for each group is equal to the whole class average: 80%
$H_1:$ the attendance for some groups is not equal to the whole class average: 80%
Total: 4 groups with 100 students each.
Observed values for each group:
Group 1: $100\times0.84=84$
Group 2: $100\times0.81=81$
Group 3: $100\times0.78=78$
Group 4: $100\times0.76=76$
Expected count of Group 1: $100\times0.80=80$
Expected count of Group 2: $100\times0.80=80$
Expected count of Group 3: $100\times0.80=80$
Expected count of Group 4: $100\times0.80=80$
$X^2=Σ\frac{(O_i-E_i)^2}{E_1}=\frac{(84-80)^2}{80}+\frac{(81-80)^2}{80}+\frac{(78-80)^2}{80}+\frac{(76-80)^2}{80}=0.463$
$k=4$. So, $d.f.=4-1=3$
$X_α^2=X_{0.05}^2=7.815$
(According to Table VII, for d.f. = 3 and area to the right of critical value = 0.05)
Since $X^2\lt X_α^2$, we do not reject the null hypothesis.
