题目
The number of emails per hour received by a helpdesk were recorded. The results for a random sample of 80 one-hour periods are shown in the table.
| Number of emails per hour | 0 | 1 | 2 | 3 | 4 | 5 | 6 | | --- | --- | --- | --- | --- | --- | --- | | Frequencies | 1 | 10 | 23 | 15 | 19 | 9 | 3 |
(a) Show that the mean number of emails per hour in the sample is 3
The manager believes that the number of emails per hour received could be modelled by a Poisson distribution.
The following table shows some of the expected frequencies.
| Number of emails per hour | Expected Frequencies |
|---|---|
| 0 | r |
| 1 | 11.949 |
| 2 | 17.923 |
| 3 | 17.923 |
| 4 | 13.443 |
| 5 | s |
| 6+ | t |
(b) Find the values of r, s and t, giving your answers to 3 decimal places.
(c) Using a 10% significance level, test whether or not a Poisson model is reasonable. You should clearly state your hypotheses, test statistic and the critical value used.
题目中文翻译
记录了帮助台每小时收到的邮件数量。随机抽取的 80 个一小时区间的结果如下表。
| 每小时邮件数 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | | --- | --- | --- | --- | --- | --- | --- | | 频数 | 1 | 10 | 23 | 15 | 19 | 9 | 3 |
(a) 证明样本中每小时邮件数的平均值为 3。
经理认为，每小时收到的邮件数量可以用泊松分布来建模。
下表给出了一些期望频数。
| 每小时邮件数 | 期望频数 |
|---|---|
| 0 | r |
| 1 | 11.949 |
| 2 | 17.923 |
| 3 | 17.923 |
| 4 | 13.443 |
| 5 | s |
| 6+ | t |
(b) 求 r、s 和 t 的值，答案保留 3 位小数。
(c) 在 10% 显著性水平下，检验泊松模型是否合理。 你应清楚写出原假设、检验统计量和所用的临界值。