Answer
$X^2\gt X_α^2$: the null hypothesis is rejected. There is enough evidence that wearing a helmet causes a different distribution of injuries than not wearing one.
Work Step by Step
Total: $2068~riders$
Expected count of Multiple Locations: $2068\times0.57=1178.76$
Expected count of Head: $2068\times0.31=641.08$
Expected count of Neck: $2068\times0.03=62.04$
Expected count of Thorax: $2068\times0.06=124.08$
Expected count of Abdomen/Lumbar/Spine: $2068\times0.03=62.04$
$X^2=Σ\frac{(O_i-E_i)^2}{E_1}=\frac{(1036-1178.76)^2}{1178.76}+\frac{(864-641.08)^2}{641.08}+\frac{(38-62.04)^2}{62.04}+\frac{(83-124.08)^2}{124.08}+\frac{(47-62.04)^2}{62.04}=121.367$
$k=5$. So, $d.f.=5-1=4$
$X_α^2=X_{0.05}^2=9.488$
(According to Table VII, for d.f. = 5 and area to the right of critical value = 0.05)
Since $X^2\gt X_α^2$, we reject the null hypothesis.
