题目
Problem
Chen is treating vines to prevent fungus appearing. One month after the treatment, Chen monitors the vines to see if fungus is present.
The contingency table shows information about the type of treatment for a sample of 150 vines and whether or not fungus is present.
| Type of treatment | None | Sulphur | Copper sulphate |
|---|---|---|---|
| No fungus present | 20 | 55 | 48 |
| Fungus present | 10 | 8 | 9 |
Test, at the 5% level of significance, whether or not there is any association between the type of treatment and the presence of fungus. Show your working clearly, stating your hypotheses, expected frequencies, test statistic and critical value.
(8)
(Total for Question 1 is 8 marks)
题目中文翻译
Chen 正在对葡萄藤进行处理，以防止真菌出现。处理一个月后， Chen 观察葡萄藤上是否有真菌。
列联表给出了一个 150 棵葡萄藤样本中处理类型以及是否有真菌的信息。
| 处理类型 | 不处理 | 硫磺 | 硫酸铜 |
|---|---|---|---|
| 无真菌 | 20 | 55 | 48 |
| 有真菌 | 10 | 8 | 9 |
在 5% 显著性水平下，检验处理类型与是否有真菌之间是否存在关联。 请清楚写出你的过程，并写出原假设、期望频数、检验统计量和临界值。