题目
Chris runs boat trips between two islands during the summer. During her trips, Chris claims that whales are seen randomly at a mean rate of 2 in every 9 trips.
To investigate Chris’s claim, a random sample of 18 boat trips run by Chris was taken.
(a) Using a 5% level of significance, find the critical region, for a two-tailed test, to enable Chris to test her claim.
(b) State the actual level of significance of this test.
The total number of whales seen in the 18 boat trips was 6
(c) State what this suggests about Chris’s claim. Give a reason for your answer.
The following summer, Chris decides to run n trips so that the probability of her seeing at least one whale is more than 0.9
(d) Assuming Chris’s claim is true, find the minimum value of n.
Chris believes that she sees fewer whales during the winter. A random sample of 45 trips run in the winter was taken and the total number of whales seen was 5
(e) Test, at the 5% level of significance, whether or not the mean rate of whales seen in winter is less than 2 in every 9 trips. State your hypotheses clearly.
(Total for Question 3 is 13 marks)
题目中文翻译
Chris 夏天经营两岛之间的船程。她声称，在她的航程中，鲸鱼随机出现的平均速率为每 9 次航程 2 次。
为了检验这一说法，随机抽取了 Chris 经营的 18 次航程。
(a) 使用 5% 显著性水平，求双尾检验的临界域，以便 Chris 检验她的说法。
(b) 写出该检验的实际显著性水平。
18 次航程中观察到的鲸鱼总数为 6。
(c) 说明这对 Chris 的说法意味着什么，并给出理由。
第二个夏天，Chris 决定安排 n 次航程，使她看到至少一只鲸鱼的概率大于 0.9。
(d) 假设 Chris 的说法为真，求 n 的最小值。
Chris 认为她在冬天看到的鲸鱼更少。冬天随机抽取了 45 次航程，总共看到 5 只鲸鱼。
(e) 在 5% 显著性水平下检验冬天每 9 次航程看到鲸鱼的平均速率是否小于 2 次，并清楚写出假设。
（第 3 题共 13 分）