一位研究人员声称，老年人对突然出现的巨大噪声作出反应所需的时间比年轻人更长。为了调查这一点，研究人员随机选取 6 名 50 岁以上的人和 8 名 25 岁以下的人，并记录他们对突然出现的巨大噪声的反应时间，单位为毫秒。反应时间如下。

在 5% 显著性水平下进行 Wilcoxon 秩和检验，检验这位研究人员的声称。

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

把两组反应时间合并并从大到小排名。若年长组更慢，它的反向秩和应偏小。

Under the common-shape location model, let $H_0$ be that the population medians are equal and $H_1$ that the over-50 population has a higher median. Assigning rank $1$ to the smallest time gives the following pooled ranks in the data order.

The older group’s ascending rank sum is $5+8+9+11+13+14=60$. Reversing the ranks replaces each rank $r$ by $15-r$, giving ranks $10,7,6,4,2,1$ and sum

A longer reaction time corresponds to a smaller reversed rank, so evidence for the claim is a small value of $R'$. For sample sizes $6$ and $8$, the lower one-sided $5\%$ critical value for the size-$6$ rank sum is $31$. Since $30\le31$, we reject $H_0$. There is sufficient evidence at the $5\%$ level that the older group tends to take longer to react.