题目
On Friday evenings, a shop opens from 7 pm to 11 pm. During this time customers are known to enter the shop at a mean rate of 20 per hour.
(a) State a suitable distribution to model the number of customers that enter this shop in a 30-minute interval on Friday evenings.
(b) State a necessary assumption for the model in part (a) to be valid.
The manager makes alterations to the shop’s layout. Following these alterations, the manager wants to find out whether the mean rate of customers entering the shop has changed.
To test this, the manager decides to monitor the number of customers entering the shop the following Friday. The manager randomly selects a 30-minute interval between 7 pm and 11 pm.
(c) Write down suitable null and alternative hypotheses that the manager should use.
(d) Using a 3% level of significance, find the critical region for the manager’s test.
(e) Find the actual significance level of this test based on your critical region from part (d)
During the 30-minute interval that the manager monitored, 16 customers entered the shop.
(f) Comment on this finding in the light of your critical region found in part (d)
(Total for Question 2 is 10 marks)
题目中文翻译
周五晚上，一家商店从晚上 7 点营业到 11 点。在此期间，已知顾客以每小时 20 人的平均速率进入商店。
(a) 说明一个合适的分布来建模周五晚上 30 分钟内进入商店的顾客数量。
(b) 说明 (a) 中模型有效所需的一个必要假设。
经理对商店布局进行了改造。改造后，经理想了解进入商店的顾客平均速率是否发生了变化。
为此，经理决定在下周五监控进入商店的顾客数量。经理在晚上 7 点到 11 点之间随机选择了一个 30 分钟的时间段。
(c) 写出经理应使用的合适原假设和备择假设。
(d) 使用 3% 的显著性水平，求此检验的临界区域。
(e) 根据你在 (d) 中的临界区域，求此检验的实际显著性水平。
在经理监控的 30 分钟内，有 16 名顾客进入了商店。
(f) 根据你在 (d) 中找到的临界区域，评论此发现。
（第 2 题共 10 分）