题目
The number of jobs sent to a printer per hour in a small office is recorded for 120 hours. The results are summarised in the following table.
| Number of jobs | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Frequency | 24 | 34 | 28 | 21 | 8 | 5 |
(a) Show that the mean number of jobs sent to the printer per hour for these data is 1.75
The office manager believes that the number of jobs sent to the printer per hour can be modelled using a Poisson distribution. The office manager uses the mean given in part (a) to calculate the expected frequencies for this model. Some of the results are given in the following table.
| Number of jobs | 0 | 1 | 2 | 3 | 4 | 5 or more |
|---|---|---|---|---|---|---|
| Expected frequency | 20.85 | 36.49 | 31.93 | r | s | 3.95 |
(b) Show that the value of s is 8.15 to 2 decimal places.
(c) Find the value of r to 2 decimal places.
The value of for the first four frequencies in the table is 1.43
(d) Test, at the 5% level of significance, whether or not the number of jobs sent to the printer per hour can be modelled using a Poisson distribution. Show your working clearly, stating your hypotheses, test statistic and critical value.
题目中文翻译
某小型办公室记录了 120 小时内每小时送往打印机的作业数量。 结果汇总如下表。
| 作业数 | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 频数 | 24 | 34 | 28 | 21 | 8 | 5 |
(a) 证明这些数据中每小时送往打印机的作业平均数为 1.75。
办公室经理认为，每小时送往打印机的作业数量可以用泊松分布建模。 经理使用 (a) 小题中的平均数计算该模型的期望频数。 部分结果如下表。
| 作业数 | 0 | 1 | 2 | 3 | 4 | 5 或以上 |
|---|---|---|---|---|---|---|
| 期望频数 | 20.85 | 36.49 | 31.93 | r | s | 3.95 |
(b) 证明 s 的值为 8.15，保留到 2 位小数。
(c) 求 r 的值，保留到 2 位小数。
表中前四个频数对应的 的值为 1.43。
(d) 在 5% 显著性水平下检验每小时送往打印机的作业数量是否可以用泊松分布建模。 请清楚写出你的原假设、检验统计量和临界值。