| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | A. |
A |
| deepseekr1 | Answer: A The department store's claim that over 60% of visitors shop there corresponds to the alternative hypothesis (Ha: p > 0.60). The null hypothesis (H0) must be the complementary statement (p ≤ 0.60). This aligns with **Option A**, where H0 and Ha are correctly specified for a one-tailed test supporting the claim. Other options either use incorrect equality conditions (B, C) or reverse the hypotheses (D). |
A |
| gpto1 | A | A |
| GPT-4o | A. H0: p ≤ 0.60 and Ha: p > 0.60 | A |
| llama3.1-70B-Instruct | A |
A |
| llama3.1-405B-Instruct | A. |
A |
| DeepSeek-Coder-V2 | A | A |
| Qwen2-72B-Instruct | A. H0: p ≤ 0.60 and Ha: p > 0.60 | A |
| baichuan4 | A. H0: p ≤ 0.60 and Ha: p > 0.60 | A |
| doubao | A The claim is that over 60 percent of the mall's visitors shop at that store, so the null hypothesis (H0) should be that the proportion is less than or equal to 0.60 and the alternative hypothesis (Ha) should be that the proportion is greater than 0.60. |
A |
| minimax | A. H0: p ≤ 0.60 and Ha: p > 0.60 The null hypothesis (H0) is typically the statement that there is no effect or no difference, and the alternative hypothesis (Ha) is the statement that there is an effect or a difference. In this case, the department store is claiming that more than 60 percent of the visitors shop there, so the null hypothesis would be that the proportion is less than or equal to 60 percent, and the alternative hypothesis would be that the proportion is greater than 60 percent. |
A |
| kimi | A. H0: p ≤ 0.60 and Ha: p > 0.60 | A |
| wenxinyiyan | A Explanation: In statistics, when we want to test a claim, we typically set up two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha). * The null hypothesis (H0) is the hypothesis that we assume to be true until we have enough evidence to reject it. It often represents the "status quo" or the "default" position. * The alternative hypothesis (Ha) is the hypothesis that we are trying to prove with our test. It represents the new or alternative position that we are investigating. In this question, the department store claims that "over 60 percent of the mall’s visitors shop at that store." This means they are claiming that the proportion p is greater than 0.60. To test this claim, we would set up the null hypothesis as the opposite of what they are claiming, i.e., that the proportion is less than or equal to 0.60. And the alternative hypothesis would be what they are claiming, i.e., that the proportion is greater than 0.60. So, the correct pair of hypotheses would be: H0: p ≤ 0.60 (the proportion is less than or equal to 0.60) Ha: p > 0.60 (the proportion is greater than 0.60) This corresponds to option A. |
A |
| zhipu | A The department store's claim is that "over 60 percent of the mall’s visitors shop at that store." This means they are asserting that the proportion \( p \) is greater than 0.60. To test this claim, we set up our hypotheses as follows: - The null hypothesis (\( H_0 \)) typically represents the status quo or the claim to be tested. In this case, it would be that the proportion is 60 percent or less. - The alternative hypothesis (\( H_a \)) represents the claim we are trying to find evidence for, which is that the proportion is greater than 60 percent. Thus, the appropriate pair of hypotheses would be: A. \( H_0: p \leq 0.60 \) and \( H_a: p > 0.60 \) This pair correctly reflects the claim that the department store is making. |
A |
| gpto1 | A | A |
| deepseekv3 | The correct answer is: **A. H0: p ≤ 0.60 and Ha: p > 0.60** Explanation: The department store's claim is that **over 60 percent** of the mall’s visitors shop at the store. This is a one-sided alternative hypothesis, which corresponds to \( H_a: p > 0.60 \). The null hypothesis \( H_0 \) should represent the opposite of the claim, which is \( p \leq 0.60 \). Therefore, the correct pair of hypotheses is \( H_0: p \leq 0.60 \) and \( H_a: p > 0.60 \). |
A |