题目
Andy has some apple trees. Over many years she has graded each apple from her trees as A, B, C, D or E according to the quality of the apple, with A being the highest quality and E being the lowest quality.
She knows that the proportion of apples in each grade produced by her trees is as follows.
| Grade | A | B | C | D | E |
|---|---|---|---|---|---|
| Proportion | 4% | 28% | 52% | 10% | 6% |
Raj advises Andy to add potassium to the soil around her apple trees.
Andy believes that adding potassium will not affect the distribution of grades for the quality of the apples.
To test her belief Andy adds potassium to the soil around her trees. The following year she counts the number of apples in each grade. The number of apples in each grade is shown in the table below.
| Grade | A | B | C | D | E |
|---|---|---|---|---|---|
| Frequency | 9 | 71 | 136 | 21 | 3 |
Test Andy’s belief using a 5% level of significance. Show your working clearly, stating your hypotheses, expected frequencies and degrees of freedom.
题目中文翻译
Andy 有一些苹果树。多年来，她会根据苹果质量把树上每个苹果分成 A、B、C、D 或 E 级，其中 A 级最高，E 级最低。
她知道她的苹果树所生产苹果在各等级中的比例如下。
| 等级 | A | B | C | D | E |
|---|---|---|---|---|---|
| 比例 | 4% | 28% | 52% | 10% | 6% |
Raj 建议 Andy 在苹果树周围的土壤中加入钾。
Andy 认为加入钾不会影响苹果质量等级的分布。
为检验她的想法，Andy 在苹果树周围加入钾。第二年她统计了每个等级的苹果数量。各等级数量如下表。
| 等级 | A | B | C | D | E |
|---|---|---|---|---|---|
| 频数 | 9 | 71 | 136 | 21 | 3 |
在 5% 显著性水平下检验 Andy 的想法。清楚写出你的工作过程，说明假设、期望频数和自由度。