A study investigates the effectiveness of a new safety helmet for cyclists. Out of $1800$ cyclists not wearing the new helmet, $27$ suffered serious head injuries. Out of $5400$ cyclists wearing the new helmet, $9$ suffered serious head injuries. At the $0.05$ significance level, test the claim using a hypothesis test that the new helmet reduces the risk of serious head injury.

Since the $Z$-statistic $\left(6.946\right)$ exceeds the critical value $\left(1.645\right)$, we reject the null hypothesis (no difference in injury rates). This means there is sufficient evidence at the $0.05$ significance level to support the claim that the new helmet reduces the risk of serious head injuries for cyclists.

Since the $Z$-statistic $\left(1.55\right)$ does not exceed the critical value $\left(1.645\right)$, we fail to reject the null hypothesis (no difference in injury rates). This means there is insufficient evidence at the $0.05$ significance level to support the claim that the new helmet reduces the risk of serious head injuries for cyclists.