Answer
$X^2\lt X_α^2$: the null hypothesis is not rejected.
There is no significant difference among the groups in attendance patterns.
Work Step by Step
$H_0:$ the attendance for each group is equal to the whole class average: 83%
$H_1:$ the attendance for some groups is not equal to the whole class average: 83%
Total: 4 groups with 100 students each.
Observed values for each group
Group 1: $100\times0.84=84$
Group 2: $100\times0.84=84$
Group 3: $100\times0.84=84$
Group 4: $100\times0.81=81$
Expected count of Group 1: $100\times0.83=83$
Expected count of Group 2: $100\times0.83=83$
Expected count of Group 3: $100\times0.83=83$
Expected count of Group 4: $100\times0.83=83$
$X^2=Σ\frac{(O_i-E_i)^2}{E_1}=\frac{(84-83)^2}{83}+\frac{(84-83)^2}{83}+\frac{(84-83)^2}{83}+\frac{(81-83)^2}{83}=0.084$
$k=4$. 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.
