题目
A meteor shower occurs for several weeks every summer. One Monday night during this meteor shower, Chris goes out to look for meteors and sees an average of 15 meteors per hour.
(a) Find the probability that in a random 20-minute period of time on this Monday night Chris sees
(i) at least 6 meteors,
(ii) no more than 3 meteors.
Chris is told by the local astronomy club that there will be more meteors to be seen per hour on the following Friday night than on Monday night.
Chris decides to use data from the Friday night to test, at a 5% significance level, if there is evidence to support the claim of the local astronomy club.
Chris plans to spend 30 minutes looking for meteors on the Friday night.
(b) Write down suitable null and alternative hypotheses that Chris can use.
(c) Find the critical region for the test and state its associated probability.
On the Friday night, Chris sees 12 meteors in the 30 minutes.
(d) State the conclusion to the test that can be made using this observation. Give a reason for your answer.
(Total for Question 5 is 10 marks)
题目中文翻译
每年夏天会有几周的流星雨。在这个流星雨期间的一个周一晚上，Chris 出去看流星，平均每小时看到 15 颗流星。
(a) 求在这个周一晚上的随机 20 分钟内，Chris 看到以下情况的概率
(i) 至少 6 颗流星，
(ii) 不超过 3 颗流星。
Chris 从当地天文俱乐部得知，下周五晚上每小时能看到的流星比周一晚上多。
Chris 决定使用周五晚上的数据在 5% 的显著性水平下检验是否有证据支持当地天文俱乐部的声明。
Chris 计划在周五晚上花 30 分钟看流星。
(b) 写出 Chris 可以使用的合适原假设和备择假设。
(c) 求此检验的临界区域并说明其关联概率。
在周五晚上，Chris 在 30 分钟内看到了 12 颗流星。
(d) 说明可以使用此观察结果得出的检验结论。给出你的理由。
（第 5 题共 10 分）