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 by constructing an appropriate confidence interval that the new helmet reduces the risk of serious head injury.

• A. The $90\%$ one-tailed confidence interval for the difference $p_1-p_2$ is approximately $(0.00853,0.01813)$, which supports the claim that the helmet reduces the risk of serious head injury.
• B. The $95\%$ one-tailed confidence interval for the difference $p_1-p_2$ is approximately $(-0.0085,\infty )$, which supports the claim that the helmet increases the risk of serious head injury.
• C. The $95\%$ two-tailed confidence interval includes $0$, so there is not enough evidence to support the claim that the helmet is effective.
• D. The $95\%$ one-tailed confidence interval for the difference $p_1-p_2$ is approximately $(0,0.0085)$, which shows no significant difference in injury rates.

Answer: (A)