| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | D. The power of a test concerns its ability to detect an alternative hypothesis. |
D |
| deepseekr1 | D. The power of a test concerns its ability to detect an alternative hypothesis. **Explanation:** - **A** is false because rejecting at a higher significance level (10%) does not guarantee rejection at a stricter level (5%). - **B** is false because the choice between one- and two-sided tests should be based on prior hypotheses, not post-data analysis. - **C** is false because the significance level (1%) refers to the Type I error rate (rejecting a true null hypothesis), not the overall probability of rejection. - **D** is true as power measures the test’s ability to correctly reject the null hypothesis when the alternative is true. **Answer:** D |
D |
| gpto1 | Answer: D | D |
| GPT-4o | D. | D |
| llama3.1-70B-Instruct | D |
D |
| llama3.1-405B-Instruct | D. The power of a test concerns its ability to detect an alternative hypothesis. This is a true statement about hypothesis testing. The power of a test is defined as the probability that the test correctly rejects a false null hypothesis, which is equivalent to the ability to detect an alternative hypothesis when it is true. The other options are incorrect: A. If there is sufficient evidence to reject a null hypothesis at the 10% level, it does not necessarily mean there is sufficient evidence to reject it at the 5% level. The significance level (alpha) determines how strong the evidence must be to reject the null hypothesis, and a lower alpha (e.g., 5% vs. 10%) requires stronger evidence. B. Whether to use a one- or a two-sided test should be decided before the data are gathered, based on the research question and the nature of the hypothesis being tested. This decision affects the calculation of the test statistic and p-value. C. If a hypothesis test is conducted at the 1% level, it means that there is a 1% chance of rejecting the null hypothesis if it is actually true (Type I error). However, this does not mean there is a 1% chance of rejecting the null hypothesis in general. The probability of rejecting the null hypothesis also depends on the sample data and the test statistic. |
D |
| DeepSeek-Coder-V2 | D | D |
| Qwen2-72B-Instruct | D. The power of a test concerns its ability to detect an alternative hypothesis. | D |
| baichuan4 | D | D |
| doubao | D A is incorrect as sufficient evidence to reject at 10% level doesn't mean sufficient at 5% level. B is incorrect as the type of test should be decided before data collection. C is incorrect as the 1% is the significance level, not the chance of rejecting the null hypothesis. D is the correct statement about the power of a test. |
D |
| minimax | D. The power of a test concerns its ability to detect an alternative hypothesis. | D |
| kimi | D. The power of a test concerns its ability to detect an alternative hypothesis. Explanation: A. This statement is false. A more stringent level (lower alpha level) like 5% requires stronger evidence to reject the null hypothesis than a less stringent level like 10%. B. This statement is false. The decision to use a one- or two-sided test is typically made before collecting data, based on the research question and hypotheses. C. This statement is misleading. A 1% level of significance means that there is a 1% chance of rejecting the null hypothesis when it is true (Type I error), not a 1% chance of rejecting it in general. D. This statement is true. The power of a test is the probability that it correctly rejects a false null hypothesis, which is related to the ability to detect the alternative hypothesis. |
D |
| wenxinyiyan | D Explanation: A. This is false. If there is sufficient evidence to reject a null hypothesis at the 10% level, it does not necessarily mean there is sufficient evidence to reject it at the 5% level. The significance level (α) determines how strict the criteria are for rejecting the null hypothesis. A lower α (e.g., 5%) requires stronger evidence to reject the null than a higher α (e.g., 10%). B. This is false. Whether to use a one- or a two-sided test should be decided before the data are gathered, based on the research question and hypothesis. C. This is false. The significance level (e.g., 1%) represents the maximum acceptable probability of rejecting the null hypothesis when it is actually true (i.e., type I error). It does not represent the probability of rejecting the null hypothesis in general. D. This is true. The power of a test refers to its ability to correctly reject the null hypothesis when it is false, i.e., its ability to detect an alternative hypothesis. |
D |
| zhipu | D Explanation: - A is incorrect because if there is sufficient evidence to reject a null hypothesis at the 10% level, it does not necessarily mean there is sufficient evidence to reject it at the 5% level. The 5% level is more stringent. - B is incorrect because the decision to use a one- or a two-sided test should be made before the data are gathered, based on the research question and hypotheses. - C is incorrect because the 1% level refers to the significance level (alpha), which is the probability of rejecting the null hypothesis when it is actually true (Type I error), not the chance of rejecting the null hypothesis in general. - D is correct because the power of a test is the probability that it correctly rejects a false null hypothesis (i.e., detects an alternative hypothesis when it is true). |
D |
| gpto1 | Answer: D | D |
| deepseekv3 | The correct answer is: **D. The power of a test concerns its ability to detect an alternative hypothesis.** Explanation: - **A** is false because rejecting the null hypothesis at the 10% level does not guarantee rejection at the 5% level (a stricter criterion). - **B** is false because the decision to use a one- or two-sided test should be made before gathering data, based on the research question. - **C** is false because the significance level (1%) refers to the probability of rejecting the null hypothesis when it is true (Type I error), not the overall chance of rejection. - **D** is true because the power of a test measures its ability to correctly reject the null hypothesis when the alternative hypothesis is true. |
D |