题目
Problem
In the colleges in three regions of a particular country, students are given individual targets to achieve. Their performance is measured against their individual target and graded as ‘above target’, ‘on target’ or ‘below target’. For a random sample of students from each of the three regions, the observed frequencies are summarised in the following table.
| Performance | Region A | Region B | Region C | Total |
|---|---|---|---|---|
| Above target | 62 | 41 | 44 | 147 |
| On target | 102 | 94 | 95 | 291 |
| Below target | 56 | 45 | 61 | 162 |
| Total | 220 | 180 | 200 | 600 |
Test, at the 10% significance level, whether performance is independent of region.
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题目中文翻译
在某个国家三个地区的学院中，学生会被给予各自需要达到的个人目标。他们的表现会根据个人目标进行衡量，并被评为“高于目标”、“达到目标”或“低于目标”。从三个地区分别随机抽取学生，观测频数汇总如下表。
| 表现 | 地区 A | 地区 B | 地区 C | 总计 |
|---|---|---|---|---|
| 高于目标 | 62 | 41 | 44 | 147 |
| 达到目标 | 102 | 94 | 95 | 291 |
| 低于目标 | 56 | 45 | 61 | 162 |
| 总计 | 220 | 180 | 200 | 600 |
在 10% 显著性水平下，检验表现是否与地区独立。