题目
Scientists are studying the effects of exercise on LDL blood cholesterol levels. Over a three-month period, a large group of people exercised for 20 minutes each day. For a randomly chosen sample of 10 of these people, the LDL blood cholesterol levels were measured at the beginning and the end of the three-month period. The results, measured in suitable units, are as follows.
| Person | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| Cholesterol level Beginning | 72 | 84 | 120 | 90 | 102 | 135 | 64 | 75 | 80 | 88 |
| Cholesterol level End | 64 | 76 | 105 | 92 | 105 | 115 | 67 | 75 | 75 | 84 |
(a) Test, at the 2.5% significance level, whether there is evidence that the population mean LDL blood cholesterol level has reduced by more than 2 units after the three-month period.
(b) State any assumption that you have made in part (a).
题目中文翻译
科学家正在研究运动对 LDL 血液胆固醇水平的影响。在三个月期间，一大组人每天运动 20 分钟。从这些人中随机选取 10 人，分别在三个月开始和结束时测量 LDL 血液胆固醇水平。结果用合适单位表示如下。
| 人 | A | B | C | D | E | F | G | H | I | J |
|---|---|---|---|---|---|---|---|---|---|---|
| 胆固醇水平 开始 | 72 | 84 | 120 | 90 | 102 | 135 | 64 | 75 | 80 | 88 |
| 胆固醇水平 结束 | 64 | 76 | 105 | 92 | 105 | 115 | 67 | 75 | 75 | 84 |
(a) 在 2.5% 显著性水平下，检验是否有证据表明三个月后总体平均 LDL 血液胆固醇水平降低了超过 2 个单位。
(b) 写出你在(a)中所作的任何假设。