$2025$ - $2026$ 学年 医学科学素养Ⅱ 大题示例
基础医学专业课 课堂讲解
2025.10.9, 不计分, 不作考勤
一、 A study measures the blood pressure of 10 patients before and after a new treatment. The blood pressure readings (in mmHg) are as follows:
- Before treatment: 120, 135, 142, 130, 126, 138, 145, 150, 140, 132
- After treatment: 118, 130, 138, 125, 124, 135, 140, 148, 138, 130
Perform a paired t-test to determine if the treatment has a significant effect on blood pressure. Use a significance level of 0.05.
| Mean | Standard Deviation | |
|---|---|---|
| Before Treatment | 135.8 | 9.08 |
| After Treatment | 132.6 | 8.91 |
| Difference | 3.2 | 1.40 |
-
Is this a one-tailed test or two-tailed test?
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What are the degrees of freedom?
-
Please perform the test and draw a conclusion (alpha = 0.05).
二、 Please use t-test to determine if there is a significant difference between the fitness results for football players and ballet dancers (alpha = 0.05).
| Ballet Dancers | Football Players |
|---|---|
| 89.2 | 79.3 |
| 78.2 | 78.3 |
| 89.3 | 85.3 |
| 88.3 | 79.3 |
| 87.3 | 88.9 |
| 90.1 | 91.2 |
| 95.2 | 87.2 |
| 94.3 | 89.2 |
| 78.3 | 93.3 |
| 89.3 | 79.9 |
Sample statistics:
- \(\bar{x}_1 = 87.95\), \(\bar{x}_2 = 85.19\)
- \(s_1^2 = 32.38\), \(s_2^2 = 31.18\)
三、 A drug company tested three formulations of a pain relief medicine for migraine headache sufferers. For the experiment, 27 volunteers were selected and 9 were randomly assigned to one of three drug formulations. The subjects were instructed to take the drug during their next migraine headache episode and to report their pain on a scale of 1 to 10 (10 being most pain). Are they equal?
| Type of Drug | Pain Scores | Sample Mean | Sample SD |
|---|---|---|---|
| A | 4, 5, 4, 3, 2, 4, 3, 4, 4 | 3.67 | 0.87 |
| B | 6, 8, 4, 5, 4, 6, 5, 8, 6 | 5.78 | 1.48 |
| C | 6, 7, 6, 6, 7, 5, 6, 5, 5 | 5.89 | 0.78 |
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What hypothesis testing method should be used?
-
What are the degrees of freedom?
-
Please perform the test and draw a conclusion (alpha = 0.05).
四、 We would love to use Chi-square test to determine if there is a statistical difference in the amount of illness between those who ate tomatoes and those who did not on a cruise ship.
| Disease | No Disease | Total | |
|---|---|---|---|
| Tomatoes | 40 | 40 | 80 |
| No Tomatoes | 80 | 60 | 140 |
| Total | 120 | 100 | 220 |
-
What are the degrees of freedom?
-
Please fill in the following table with the expected frequencies (keep two decimals):
| Disease | No Disease | |
|---|---|---|
| Tomatoes | ||
| No Tomatoes | ||
- Please perform the Chi-square test and draw a conclusion (alpha = 0.05).
五、 An instructor wants to use two exams in her classes next year. This year, she gives both exams to the students. She wants to know if the exams are equally difficult and wants to check this by looking at the differences between scores. If the mean difference between scores for students is "close enough" to zero, she will make a practical conclusion that the exams are equally difficult.
Here is the data:
| ID | Exam 1 Score | Exam 2 Score | Difference |
|---|---|---|---|
| 1 | 63 | 69 | 6 |
| 2 | 65 | 65 | 0 |
| 3 | 56 | 62 | 6 |
| 4 | 100 | 91 | -9 |
| 5 | 88 | 78 | -10 |
| 6 | 83 | 87 | 4 |
| 7 | 77 | 79 | 2 |
| 8 | 92 | 88 | -4 |
| 9 | 90 | 85 | -5 |
| 10 | 84 | 92 | 8 |
| 11 | 68 | 69 | 1 |
| 12 | 74 | 81 | 7 |
| 13 | 87 | 84 | -3 |
| 14 | 64 | 75 | 11 |
| 15 | 71 | 84 | 13 |
| 16 | 88 | 82 | -6 |
| SUM | 1250 | 1271 | 21 |
| MEAN | 78.13 | 79.44 | 1.31 |
| Standard deviation | 12.66 | 9.15 | 7.00 |
-
What hypothesis method should be applied to find out whether the two exams are equally difficult or not?
-
What are the degrees of freedom?
-
Please test the hypotheses and draw a conclusion (alpha = 0.01).