题目
Problem
Two companies, P and Q, produce a certain type of paint brush. An independent examiner rates the quality of the brushes produced as poor, satisfactory or good. He takes a random sample of brushes from each company. The examiner’s ratings are summarised in the table.
| Company | Poor | Satisfactory | Good |
|---|---|---|---|
| P | 18 | 43 | 64 |
| Q | 22 | 22 | 31 |
(a) Test, at the 5% significance level, whether quality of brushes is independent of company.
[7]
(b) Compare the quality of the brushes produced by the two companies.
[1]
题目中文翻译
两家公司 P 和 Q 生产某种油漆刷。一名独立检查员将所生产油漆刷的质量评为差、合格或好。他从每家公司随机抽取油漆刷样本。检查员的评分概括如下表。
| 公司 | 差 | 合格 | 好 |
|---|---|---|---|
| P | 18 | 43 | 64 |
| Q | 22 | 22 | 31 |
(a) 在 5% 显著性水平下，检验油漆刷质量是否与公司相互独立。
(b) 比较两家公司生产的油漆刷质量。