| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | D. I and II |
D |
| deepseekr1 | D. I and II **Answer:** D The power of a hypothesis test increases when: 1. **Increasing the sample size (I)** reduces variability, making it easier to detect an effect. 2. **Increasing the significance level (II)** (e.g., from α = 0.05 to α = 0.10) lowers the threshold for rejecting the null hypothesis, thereby increasing power. 3. **Increasing the probability of a Type II error (III)** directly reduces power (since power = 1 - β), making III incorrect. Thus, the correct choices are **I and II**, corresponding to option **D**. |
D |
| gpto1 | D | D |
| GPT-4o | D. I and II | D |
| llama3.1-70B-Instruct | D |
D |
| llama3.1-405B-Instruct | D. I and II |
D |
| DeepSeek-Coder-V2 | D. I and II | D |
| Qwen2-72B-Instruct | D. I and II | D |
| baichuan4 | D. I and II | D |
| doubao | D. I and II. Increasing the sample size generally increases the power of a test. Increasing the significance level also increases the power. Increasing the probability of a Type II error decreases the power. So I and II are correct. | D |
| minimax | D. I and II Increasing the sample size generally increases the power of a hypothesis test because it reduces the variability of the sample statistic, making it easier to detect an effect if one exists. Increasing the significance level (alpha) also increases the power of the test because it makes the rejection region larger, thus making it easier to reject the null hypothesis. However, increasing the probability of a Type II error (beta) would actually decrease the power of the test, as power is defined as 1 - beta. Therefore, the correct answer is I and II, but it's important to note that III is incorrect because it would decrease, not increase, the power. |
D |
| kimi | D. I and II | D |
| wenxinyiyan | D. I and II Explanation: The power of a hypothesis test is the probability of correctly rejecting a false null hypothesis. It is influenced by several factors, including sample size, significance level, and the effect size. I. Increasing the sample size: As the sample size increases, the power of the test also increases. This is because a larger sample size provides more information about the population, making it easier to detect a significant effect if it exists. II. Increasing the significance level: The significance level (often denoted as α) is the probability of rejecting the null hypothesis when it is actually true (i.e., committing a Type I error). However, increasing the significance level also increases the power of the test because it raises the threshold for what is considered "significant." In other words, you are more willing to reject the null hypothesis, which increases the chances of correctly rejecting it when it is false. III. Increasing the probability of a Type II error: A Type II error occurs when you fail to reject the null hypothesis when it is actually false. Increasing the probability of a Type II error would actually decrease the power of the test, because it means you are less likely to correctly reject the null hypothesis when it is false. Therefore, increasing the sample size (I) and increasing the significance level (II) will increase the power of a hypothesis test, while increasing the probability of a Type II error (III) will decrease it. |
D |
| zhipu | D. I and II Explanation: - Increasing the sample size (I) will increase the power of a hypothesis test because it reduces the standard error, making it easier to detect a true effect. - Increasing the significance level (II) will also increase the power of a hypothesis test because it makes the criteria for rejecting the null hypothesis less stringent, thereby increasing the likelihood of detecting a true effect. - Increasing the probability of a Type II error (III) would actually decrease the power of a hypothesis test, as power is defined as 1 minus the probability of a Type II error. Therefore, the correct answer is D. I and II. |
D |
| gpto1 | D | D |
| deepseekv3 | The correct answer is: **D. I and II** Explanation: - **I. Increasing the sample size** increases the power of a hypothesis test because a larger sample size reduces the standard error, making it easier to detect a true effect. - **II. Increasing the significance level** (e.g., from 0.05 to 0.10) increases the power because it makes it easier to reject the null hypothesis, increasing the likelihood of detecting a true effect. - **III. Increasing the probability of a Type II error** decreases the power, so this does not increase the power of the test. Thus, **D. I and II** is the correct answer. |
D |