题目
A medical research team carried out an investigation into the metabolic rate, MR, of men aged between 30 years and 60 years. A random sample of 10 men was taken from this age group. The table below shows for each man his MR and his body mass index, BMI. The table also shows the rank for the level of daily physical activity, DPA, which was assessed by the medical research team. Rank 1 was assigned to the man with the highest level of daily physical activity.
| Man | A | B | C | D | E | F | G | H | I | J | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | MR (x) | 6.24 | 5.94 | 6.83 | 6.53 | 6.31 | 7.44 | 7.32 | 8.70 | 7.88 | 7.78 | | BMI (y) | 19.6 | 19.2 | 23.6 | 21.4 | 20.2 | 20.8 | 22.9 | 25.5 | 23.3 | 25.1 | | DPA rank | 10 | 7 | 9 | 8 | 6 | 3 | 1 | 4 | 5 | 2 |
[You may use Sxy = 15.1608, Sxx = 6.90181, Syy = 45.304]
(a) Calculate the value of the product moment correlation coefficient between MR and BMI for these 10 men.
(b) Use your value of the product moment correlation coefficient to test, at the 5% significance level, whether or not there is evidence of a positive correlation between MR and BMI. State your hypotheses clearly.
(c) State an assumption that must be made to carry out the test in part (b).
(d) Calculate the value of Spearman’s rank correlation coefficient between MR and DPA for these 10 men.
(e) Use a two-tailed test and a 5% level of significance to assess whether or not there is evidence of a correlation between MR and DPA.
题目中文翻译
一支医学研究团队调查了 30 至 60 岁男性的代谢率 MR。 从该年龄组中随机抽取了 10 名男性。 下表显示了每位男性的 MR、身体质量指数 BMI，以及医学研究团队评估的日常体力活动 DPA 等级。 等级 1 分配给日常体力活动水平最高的男性。
| 男性 | A | B | C | D | E | F | G | H | I | J | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | MR (x) | 6.24 | 5.94 | 6.83 | 6.53 | 6.31 | 7.44 | 7.32 | 8.70 | 7.88 | 7.78 | | BMI (y) | 19.6 | 19.2 | 23.6 | 21.4 | 20.2 | 20.8 | 22.9 | 25.5 | 23.3 | 25.1 | | DPA 等级 | 10 | 7 | 9 | 8 | 6 | 3 | 1 | 4 | 5 | 2 |
你可以使用 , , 。
(a) 求 MR 与 BMI 的积差相关系数。
(b) 利用你在 (a) 小题中的结果，在 5% 显著性水平下检验 MR 与 BMI 是否存在正相关证据。 请清楚写出原假设。
(c) 写出完成 (b) 小题检验必须作出的一个假设。
(d) 求 MR 与 DPA 的 Spearman 等级相关系数。
(e) 使用双侧检验和 5% 显著性水平，判断 MR 与 DPA 是否存在相关证据。