题目
Problem
A plant biologist claims that as the percentage moisture content of the soil in a field increases, so does the percentage plant coverage. He splits the field into equal areas labelled A, B, C, D and E and measures the percentage plant coverage and the percentage moisture content for each area. The results are shown in the table below.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| Coverage % | 10 | 12 | 25 | 0 | 6 |
| Moisture % | 30 | 20 | 40 | 10 | 25 |
(a) Calculate Spearman’s rank correlation coefficient for these data.
(5)
(b) Stating your hypotheses clearly, test at the 5% level of significance, whether or not these data provide support for the plant biologist’s claim.
(4)
题目中文翻译
一位植物学家声称，随着田地土壤含水百分比的增加，植物覆盖百分比也会增加。他把这块田地分成大小相等的 A、B、C、D、E 五个区域，并测量每个区域的植物覆盖百分比和土壤含水百分比。结果如下表。
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 覆盖率 % | 10 | 12 | 25 | 0 | 6 |
| 含水率 % | 30 | 20 | 40 | 10 | 25 |
(a) 求这些数据的 Spearman 秩相关系数。
(b) 清楚写出假设，在 5% 显著性水平下检验：这些数据是否支持这位植物学家的说法。