| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | D. The smaller the df, the better the 68-95-99.7 Rule works for t-models. |
D |
| deepseekr1 | The false statement is **D**. **Explanation:** - **A:** True. T-distributions are symmetric like the normal distribution. - **B:** True. T-distributions have lower peaks and fatter tails, making them more spread out than the normal distribution. - **C:** True. Higher degrees of freedom (df) make t-distributions resemble the normal distribution more closely. - **D:** False. Smaller df means the t-distribution deviates further from normality, making the 68-95-99.7 Rule (designed for normal distributions) less accurate. Larger df improves the rule's applicability. **Answer:** D |
D |
| gpto1 | D | D |
| GPT-4o | D. The smaller the df, the better the 68-95-99.7 Rule works for t-models. | D |
| llama3.1-70B-Instruct | D |
D |
| llama3.1-405B-Instruct | D. The smaller the df, the better the 68-95-99.7 Rule works for t-models. |
D |
| DeepSeek-Coder-V2 | D | D |
| Qwen2-72B-Instruct | D. The smaller the df, the better the 68-95-99.7 Rule works for t-models. | D |
| baichuan4 | D | D |
| doubao | D The 68-95-99.7 Rule is for the normal distribution and does not work as well for t-distributions with small df. |
D |
| minimax | D. The smaller the df, the better the 68-95-99.7 Rule works for t-models. | D |
| kimi | The statement that is false is: D. The smaller the df, the better the 68-95-99.7 Rule works for t-models. This statement is incorrect because the 68-95-99.7 Rule, also known as the empirical rule, is a general guideline for the normal distribution, not the t-distribution. As the degrees of freedom (df) decrease, the t-distribution becomes more spread out and has fatter tails, which means it deviates more from the normal distribution and the empirical rule becomes less accurate. |
D |
| wenxinyiyan | D Explanation: A. Like the normal distribution, the t-distributions are symmetric. This is true. The t-distribution, like the normal distribution, is symmetric about its mean. B. The t-distributions are lower at the mean and higher at the tails, and so are more spread out than the normal distribution. This is true, especially for small degrees of freedom (df). As the df increases, the t-distribution approaches the normal distribution. But for small df, the t-distribution has a lower peak and thicker tails. C. The greater the df, the closer the t-distributions are to the normal distribution. This is true. As the degrees of freedom (df) increase, the t-distribution becomes more and more like the standard normal distribution. D. The smaller the df, the better the 68-95-99.7 Rule works for t-models. This is false. The 68-95-99.7 Rule is an approximation for the normal distribution, stating that about 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. For the t-distribution, especially with small df, this rule does not apply well because the t-distribution has thicker tails than the normal distribution. As the df increases, the t-distribution approaches the normal distribution, and the 68-95-99.7 Rule becomes more applicable. But for small df, the rule does not work well. |
D |
| zhipu | D Explanation: The 68-95-99.7 Rule, also known as the empirical rule, applies to the normal distribution and states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. For t-distributions, especially with smaller degrees of freedom (df), this rule does not work as well because t-distributions have heavier tails and are more spread out than the normal distribution. Therefore, statement D is false. - Statement A is true because t-distributions are symmetric like the normal distribution. - Statement B is true because t-distributions have heavier tails and are more spread out than the normal distribution. - Statement C is true because as the degrees of freedom increase, the t-distribution approaches the normal distribution. |
D |
| gpto1 | D | D |
| deepseekv3 | D. The smaller the df, the better the 68-95-99.7 Rule works for t-models. This statement is false. The 68-95-99.7 Rule, which is an empirical rule for normal distributions, works better for t-distributions as the degrees of freedom (df) increase, not as they decrease. When the df are small, the t-distribution has heavier tails and is more spread out compared to the normal distribution, making the 68-95-99.7 Rule less accurate. As the df increase, the t-distribution approaches the normal distribution, and the rule becomes more applicable. |
D |