题目
The table shows the annual tea consumption, t (kg/person), and population, p (millions), for a random sample of 7 European countries.
| Country | A | B | C | D | E | F | G | | --- | --- | --- | --- | --- | --- | --- | | Annual tea consumption, t (kg/person) | 0.27 | 0.15 | 0.42 | 0.06 | 1.94 | 0.78 | 0.44 | | Population, p (millions) | 5.4 | 5.8 | 9 | 10.2 | 67.9 | 17.1 | 8.7 |
(You may use Stt = 2.486 Spp = 3026.234 Spt = 83.634)
Angela suggests using the product moment correlation coefficient to calculate the correlation between annual tea consumption and population.
(a) Use Angela’s suggestion to test, at the 5% level of significance, whether or not there is evidence of any correlation between annual tea consumption and population. State your hypotheses clearly and the critical value used.
Johan suggests using Spearman’s rank correlation coefficient to calculate the correlation between the rank of annual tea consumption and the rank of population.
(b) Calculate Spearman’s rank correlation coefficient between the rank of annual tea consumption and the rank of population.
(c) Use Johan’s suggestion to test, at the 5% level of significance, whether or not there is evidence of a positive correlation between annual tea consumption and population. State your hypotheses clearly and the critical value used.
题目中文翻译
下表给出了 7 个欧洲国家的随机样本中，年茶消费量 t（kg/人）与人口 p（百万）。
| 国家 | A | B | C | D | E | F | G |
|---|---|---|---|---|---|---|---|
| 年茶消费量 t（kg/人） | 0.27 | 0.15 | 0.42 | 0.06 | 1.94 | 0.78 | 0.44 |
| 人口 p（百万） | 5.4 | 5.8 | 9 | 10.2 | 67.9 | 17.1 | 8.7 |
（你可以使用 Stt = 2.486，Spp = 3026.234，Spt = 83.634）
Angela 建议使用积差相关系数来计算年茶消费量与人口之间的相关性。
(a) 按照 Angela 的建议，在 5% 显著性水平下检验年茶消费量与人口之间是否有相关性的证据。 请清楚写出你的原假设和所用的临界值。
Johan 建议使用 Spearman 等级相关系数来计算年茶消费量排名与人口排名之间的相关性。
(b) 计算年茶消费量排名与人口排名之间的 Spearman 等级相关系数。
(c) 按照 Johan 的建议，在 5% 显著性水平下检验年茶消费量与人口之间是否有正相关的证据。 请清楚写出你的原假设和所用的临界值。