题目
A photocopier in a school is known to break down at random at a mean rate of 8 times per week.
(a) Give a reason why a Poisson distribution could be used to model the number of breakdowns.
The headteacher of the school replaces the photocopier with a refurbished one and wants to find out if the rate of breakdowns has increased or decreased.
(b) Write down suitable null and alternative hypotheses that the headteacher should use.
The refurbished photocopier was monitored for the first week after it was installed.
(c) Using a 5% level of significance, find the critical region to test whether the rate of breakdowns has now changed.
(d) Find the actual significance level of a test based on the critical region from part (c).
During the first week after it was installed there were 4 breakdowns.
(e) Comment on this finding in the light of the critical region found in part (c).
(Total for Question 3 is 9 marks)
题目中文翻译
学校里的一台复印机已知会随机出故障，平均每周 8 次。
(a) 给出一个理由说明为什么可以用泊松分布来建模故障次数。
校长把复印机换成了一台翻新的，并想知道故障率是增加还是减少了。
(b) 写出校长应使用的合适原假设和备择假设。
翻新的复印机在安装后的第一周被监测。
(c) 使用 5% 显著性水平，求用于检验故障率是否已经改变的临界区域。
(d) 求基于 (c) 中临界区域的检验实际显著性水平。
安装后的第一周出现了 4 次故障。
(e) 结合 (c) 中的临界区域，评论这一结果。
（第 3 题共 9 分）