Answer
$X^2\lt X_α^2$: null hypothesis is not rejected.
There is not enough evidence to conclude that the teams that play in the World Series are not evenly matched.
Work Step by Step
$H_0:$ the teams that play in the World Series are evenly matched.
$H_1:$ the teams that play in the World Series are not evenly matched.
Total: $15+17+18+30=80$ years.
Expected count of 4 Games: $80\times0.125=10$
Expected count of 5 Games: $80\times0.25=20$
Expected count of 6 Games: $80\times0.3125=25$
Expected count of 7 Games: $80\times0.3125=25$
$X^2=Σ\frac{(O_i-E_i)^2}{E_1}=\frac{(15-10)^2}{10}+\frac{(17-20)^2}{20}+\frac{(18-25)^2}{25}+\frac{(30-25)^2}{25}=5.91$
$k=4$. 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.
