| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | D. It divides the interval size by 1.732. |
D |
| deepseekr1 | D. It divides the interval size by 1.732. **Explanation**: The width of a confidence interval depends on the margin of error, which is proportional to \( \frac{1}{\sqrt{n}} \), where \( n \) is the sample size. Tripling \( n \) changes \( \frac{1}{\sqrt{n}} \) to \( \frac{1}{\sqrt{3n}} = \frac{1}{\sqrt{3}} \cdot \frac{1}{\sqrt{n}} \). Since \( \sqrt{3} \approx 1.732 \), the interval size (determined by the margin of error) is divided by \( 1.732 \). Thus, the correct answer is **D**. |
D |
| gpto1 | D | D |
| GPT-4o | D. It divides the interval size by 1.732. | D |
| llama3.1-70B-Instruct | D |
D |
| llama3.1-405B-Instruct | D. It divides the interval size by 1.732. |
D |
| DeepSeek-Coder-V2 | D | D |
| Qwen2-72B-Instruct | D. It divides the interval size by 1.732. | D |
| baichuan4 | D. It divides the interval size by 1.732. | D |
| doubao | B As the sample size increases, the width of the confidence interval decreases. Tripling the sample size will approximately divide the interval size by the square root of 3, which is approximately 1.732. So tripling the sample size will approximately divide the interval size by 1.732. |
D |
| minimax | B. It divides the interval size by 3. | D |
| kimi | D. It divides the interval size by 1.732. This is because the margin of error (which is part of the confidence interval) is inversely proportional to the square root of the sample size. If you triple the sample size, you are increasing it by a factor of 3, so you are taking the square root of 3, which is approximately 1.732. This means the margin of error would be divided by 1.732, making the confidence interval narrower. |
D |
| wenxinyiyan | D Explanation: When the sample size is tripled, the standard error of the estimate typically decreases. The confidence interval is directly related to the standard error. Specifically, when all other factors are held constant, the confidence interval is proportional to the standard error. The standard error is inversely proportional to the square root of the sample size. So, if the sample size is tripled (multiplied by 3), the standard error is multiplied by the square root of 1/3 (or divided by the square root of 3), which is approximately 1/1.732. Therefore, tripling the sample size divides the confidence interval size by approximately 1.732 (assuming that the confidence level and the variability in the data remain the same). |
D |
| zhipu | D. It divides the interval size by 1.732. Explanation: The width of a confidence interval is inversely proportional to the square root of the sample size. If you triple the sample size, the width of the confidence interval is divided by the square root of 3, which is approximately 1.732. Hence, the correct answer is D. |
D |
| gpto1 | D | D |
| deepseekv3 | The correct answer is: **D. It divides the interval size by 1.732.** Explanation: The confidence interval size is inversely proportional to the square root of the sample size. If the sample size is tripled, the confidence interval size is divided by the square root of 3, which is approximately 1.732. |
D |