| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | D. 0.74 |
D |
| deepseekr1 | The problem provides two probabilities: the significance level (α = 0.05) and the Type II error rate (β = 0.26). The power of a hypothesis test is defined as the probability of correctly rejecting a false null hypothesis, which is calculated as **1 - β**. Substituting β = 0.26, the power is **1 - 0.26 = 0.74**. **Answer:** D. 0.74 |
D |
| gpto1 | D | D |
| GPT-4o | D. 0.74 | D |
| llama3.1-70B-Instruct | D |
D |
| llama3.1-405B-Instruct | D. 0.74 Reasoning: The power of a test is the probability of rejecting the null hypothesis when it is false. In this case, the probability of failing to reject the null hypothesis when it is false is 0.26, so the power of the test is 1 - 0.26 = 0.74. Note: The other options are incorrect because: A. 0.26 is the probability of failing to reject the null hypothesis when it is false, not the power of the test. B. 0.05 is the probability of rejecting the null hypothesis when it is true (Type I error), not the power of the test. C. 0.95 is the probability of not rejecting the null hypothesis when it is true (1 - Type I error), not the power of the test. |
D |
| DeepSeek-Coder-V2 | D. 0.74 | D |
| Qwen2-72B-Instruct | D. 0.74 | D |
| baichuan4 | D. 0.74 | D |
| doubao | D The power of a test is 1 minus the probability of a Type II error. The probability of a Type II error is P(failing to reject H0 when H0 is false) = 0.26. So the power is 1 - 0.26 = 0.74. |
D |
| minimax | The power of a test is defined as the probability of correctly rejecting a false null hypothesis (H0). It is given by 1 minus the probability of a Type II error (β), which is the probability of failing to reject H0 when it is false. Power = 1 - β Given that P(failing to reject H0 when H0 is false) = β = 0.26, the power of the test is: Power = 1 - 0.26 = 0.74 Therefore, the correct answer is: D. 0.74 |
D |
| kimi | The power of a hypothesis test is defined as the probability of correctly rejecting the null hypothesis when it is false. It is calculated as \(1 - \beta\), where \(\beta\) is the probability of a Type II error, which is the probability of failing to reject a false null hypothesis. Given: - \(P(\text{rejecting } H_0 \text{ when } H_0 \text{ is true}) = 0.05\) (Type I error rate, denoted as \(\alpha\)) - \(P(\text{failing to reject } H_0 \text{ when } H_0 \text{ is false}) = 0.26\) (Type II error rate, denoted as \(\beta\)) The power of the test is: \[ \text{Power} = 1 - \beta = 1 - 0.26 = 0.74 \] So the correct answer is: D. 0.74 |
D |
| wenxinyiyan | D. 0.74 Explanation: The power of a test is defined as the probability of correctly rejecting the null hypothesis (H0) when it is false. It can also be thought of as 1 minus the probability of failing to reject H0 when H0 is false. Given that P(failing to reject H0 when H0 is false) = 0.26, the power of the test is: Power = 1 - P(failing to reject H0 when H0 is false) = 1 - 0.26 = 0.74 |
D |
| zhipu | D. 0.74 The power of a hypothesis test is the probability of correctly rejecting the null hypothesis (H0) when the alternative hypothesis (H1) is true. This is calculated as 1 minus the probability of failing to reject H0 when H0 is false. Given: - P(failing to reject H0 when H0 is false) = 0.26 Therefore, the power of the test is: \[ \text{Power} = 1 - 0.26 = 0.74 \] So, the correct answer is D. 0.74. |
D |
| gpto1 | D | D |
| deepseekv3 | The power of a hypothesis test is the probability of **correctly rejecting H0 when H0 is false**, which is calculated as: \[ \text{Power} = 1 - \text{P(failing to reject H0 when H0 is false)} \] Given that P(failing to reject H0 when H0 is false) = 0.26, the power of the test is: \[ \text{Power} = 1 - 0.26 = 0.74 \] Thus, the correct answer is **D. 0.74**. |
D |