金声玉亮2.0模型评测报告

问题

There is a single choice question about econometrics. Answer the question by replying A, B, C or D.
Question: Suppose that a hypothesis test is conducted using a 5% significance level. Which of the following statements are correct?

(i) The significance level is equal to the size of the test

(ii) The significance level is equal to the power of the test

(iii) 2.5% of the total distribution will be in each tail rejection region for a 2-sided test

(iv) 5% of the total distribution will be in each tail rejection region for a 2-sided test.
A. (ii) and (iv) only
B. (i) and (iii) only
C. (i), (ii), and (iii) only
D. (i), (ii), (iii), and (iv)
Answer:

答案

模型	模型答案	正确答案
金声玉亮2.0	B. (i) and (iii) only Explanation: (i) The significance level is equal to the size of the test: Correct. The significance level (α) is the maximum probability of rejecting the null hypothesis when it is true, which is also known as the size of the test. (ii) The significance level is equal to the power of the test: Incorrect. The power of the test is the probability of rejecting the null hypothesis when it is false, which is not equal to the significance level. (iii) 2.5% of the total distribution will be in each tail rejection region for a 2-sided test: Correct. For a 2-sided test, the significance level (α) is divided equally between the two tails, so each tail has a probability of α/2 = 0.05/2 = 0.025, or 2.5%. (iv) 5% of the total distribution will be in each tail rejection region for a 2-sided test: Incorrect. As mentioned earlier, each tail has a probability of 2.5%, not 5%. Therefore, the correct answer is B. (i) and (iii) only.	B
deepseekr1	B. (i) and (iii) only Answer: B	B
gpto1	B	B
GPT-4o	B. (i) and (iii) only	B
llama3.1-70B-Instruct	B	B
llama3.1-405B-Instruct	B. (i) and (iii) only Explanation: (i) The significance level is equal to the size of the test. This statement is correct. The significance level, often denoted as alpha (α), is the probability of rejecting the null hypothesis when it is true, which is also known as the size of the test. (ii) The significance level is equal to the power of the test. This statement is incorrect. The power of the test is the probability of rejecting the null hypothesis when it is false, which is not the same as the significance level. (iii) 2.5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is correct. For a two-sided test with a 5% significance level, the rejection region is divided equally between the two tails, with 2.5% in each tail. (iv) 5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is incorrect. As mentioned earlier, for a two-sided test with a 5% significance level, the rejection region is divided equally between the two tails, with 2.5% in each tail, not 5%. Therefore, the correct answer is B. (i) and (iii) only.	B
DeepSeek-Coder-V2	B. (i) and (iii) only	B
Qwen2-72B-Instruct	B. (i) and (iii) only	B
baichuan4	B. (i) and (iii) only	B
doubao	B. (i) and (iii) only. The significance level is the probability of rejecting the null hypothesis when it is true, which is the same as the size of the test. For a 2-sided test at 5% significance level, 2.5% is in each tail rejection region. The power of the test is not equal to the significance level. And 5% is not in each tail for a 2-sided test, but split between the two tails.	B
minimax	B. (i) and (iii) only (i) The significance level is equal to the size of the test. This statement is correct because the significance level is the probability of rejecting the null hypothesis when it is actually true, which is the definition of the size of the test. (iii) 2.5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is correct because with a 5% significance level for a two-sided test, 2.5% is allocated to each tail of the distribution to maintain the overall 5% significance level. (ii) The significance level is equal to the power of the test. This statement is incorrect because the power of the test is the probability of correctly rejecting the null hypothesis when it is false, which is not necessarily equal to the significance level. (iv) 5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is incorrect because for a two-sided test with a 5% significance level, 2.5% is in each tail, not 5%. If it were 5% in each tail, the total significance level would be 10%, not 5%.	B
kimi	B. (i) and (iii) only Explanation: (i) The significance level is indeed equal to the size of the test. It represents the probability of rejecting the null hypothesis when it is actually true, which is the definition of the size of the test. (ii) This statement is incorrect. The significance level is not equal to the power of the test. The power of the test is the probability of correctly rejecting the null hypothesis when it is false, which is 1 minus the probability of a Type II error. (iii) This statement is correct for a 5% significance level two-tailed test. In a two-tailed test, the total significance level is divided equally between the two tails, so 2.5% of the distribution is in each tail. (iv) This statement is incorrect. It is the total of both tails that is 5% for a two-tailed test, not 5% in each tail.	B
wenxinyiyan	B. (i) and (iii) only Explanation: (i) The significance level is equal to the size of the test. This statement is correct. The significance level (often denoted as α) is the probability of rejecting the null hypothesis when it is actually true. It is also known as the size of the test. (ii) The significance level is equal to the power of the test. This statement is incorrect. The power of a test is the probability of rejecting the null hypothesis when it is false. It is not equal to the significance level. (iii) 2.5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is correct. For a two-sided test with a 5% significance level, the rejection region is typically split evenly between the two tails of the distribution, so each tail would have 2.5% of the total distribution. (iv) 5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is incorrect. As explained in (iii), for a two-sided test with a 5% significance level, each tail would have 2.5% of the total distribution, not 5%.	B
zhipu	B. (i) and (iii) only Explanation: (i) The significance level is indeed equal to the size of the test. The size of the test is the probability of rejecting the null hypothesis when it is true, which is also known as the significance level. (ii) The significance level is not equal to the power of the test. The power of the test is the probability of correctly rejecting the null hypothesis when it is false. (iii) For a 2-sided test with a 5% significance level, 2.5% of the total distribution will be in each tail rejection region. (iv) This statement is incorrect because for a 2-sided test with a 5% significance level, only 2.5% of the total distribution will be in each tail, not 5%. Therefore, the correct answer is B. (i) and (iii) only.	B
gpto1	B	B

模型

模型答案

正确答案

金声玉亮2.0

B. (i) and (iii) only

Explanation:

(i) The significance level is equal to the size of the test: Correct. The significance level (α) is the maximum probability of rejecting the null hypothesis when it is true, which is also known as the size of the test.

(ii) The significance level is equal to the power of the test: Incorrect. The power of the test is the probability of rejecting the null hypothesis when it is false, which is not equal to the significance level.

(iii) 2.5% of the total distribution will be in each tail rejection region for a 2-sided test: Correct. For a 2-sided test, the significance level (α) is divided equally between the two tails, so each tail has a probability of α/2 = 0.05/2 = 0.025, or 2.5%.

(iv) 5% of the total distribution will be in each tail rejection region for a 2-sided test: Incorrect. As mentioned earlier, each tail has a probability of 2.5%, not 5%.

Therefore, the correct answer is B. (i) and (iii) only.

deepseekr1

B. (i) and (iii) only

**Answer:** B

gpto1

GPT-4o

B. (i) and (iii) only

llama3.1-70B-Instruct

llama3.1-405B-Instruct

B. (i) and (iii) only

Explanation:

(i) The significance level is equal to the size of the test. This statement is correct. The significance level, often denoted as alpha (α), is the probability of rejecting the null hypothesis when it is true, which is also known as the size of the test.

(ii) The significance level is equal to the power of the test. This statement is incorrect. The power of the test is the probability of rejecting the null hypothesis when it is false, which is not the same as the significance level.

(iii) 2.5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is correct. For a two-sided test with a 5% significance level, the rejection region is divided equally between the two tails, with 2.5% in each tail.

(iv) 5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is incorrect. As mentioned earlier, for a two-sided test with a 5% significance level, the rejection region is divided equally between the two tails, with 2.5% in each tail, not 5%.

Therefore, the correct answer is B. (i) and (iii) only.

DeepSeek-Coder-V2

B. (i) and (iii) only

Qwen2-72B-Instruct

B. (i) and (iii) only

baichuan4

B. (i) and (iii) only

doubao

B. (i) and (iii) only.

The significance level is the probability of rejecting the null hypothesis when it is true, which is the same as the size of the test. For a 2-sided test at 5% significance level, 2.5% is in each tail rejection region. The power of the test is not equal to the significance level. And 5% is not in each tail for a 2-sided test, but split between the two tails.

minimax

B. (i) and (iii) only

(i) The significance level is equal to the size of the test. This statement is correct because the significance level is the probability of rejecting the null hypothesis when it is actually true, which is the definition of the size of the test.

(iii) 2.5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is correct because with a 5% significance level for a two-sided test, 2.5% is allocated to each tail of the distribution to maintain the overall 5% significance level.

(ii) The significance level is equal to the power of the test. This statement is incorrect because the power of the test is the probability of correctly rejecting the null hypothesis when it is false, which is not necessarily equal to the significance level.

(iv) 5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is incorrect because for a two-sided test with a 5% significance level, 2.5% is in each tail, not 5%. If it were 5% in each tail, the total significance level would be 10%, not 5%.

kimi

B. (i) and (iii) only

Explanation:
(i) The significance level is indeed equal to the size of the test. It represents the probability of rejecting the null hypothesis when it is actually true, which is the definition of the size of the test.

(ii) This statement is incorrect. The significance level is not equal to the power of the test. The power of the test is the probability of correctly rejecting the null hypothesis when it is false, which is 1 minus the probability of a Type II error.

(iii) This statement is correct for a 5% significance level two-tailed test. In a two-tailed test, the total significance level is divided equally between the two tails, so 2.5% of the distribution is in each tail.

(iv) This statement is incorrect. It is the total of both tails that is 5% for a two-tailed test, not 5% in each tail.

wenxinyiyan

B. (i) and (iii) only

Explanation:

(i) The significance level is equal to the size of the test. This statement is correct. The significance level (often denoted as α) is the probability of rejecting the null hypothesis when it is actually true. It is also known as the size of the test.

(ii) The significance level is equal to the power of the test. This statement is incorrect. The power of a test is the probability of rejecting the null hypothesis when it is false. It is not equal to the significance level.

(iii) 2.5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is correct. For a two-sided test with a 5% significance level, the rejection region is typically split evenly between the two tails of the distribution, so each tail would have 2.5% of the total distribution.

(iv) 5% of the total distribution will be in each tail rejection region for a 2-sided test. This statement is incorrect. As explained in (iii), for a two-sided test with a 5% significance level, each tail would have 2.5% of the total distribution, not 5%.

zhipu

B. (i) and (iii) only

Explanation:
(i) The significance level is indeed equal to the size of the test. The size of the test is the probability of rejecting the null hypothesis when it is true, which is also known as the significance level.

(ii) The significance level is not equal to the power of the test. The power of the test is the probability of correctly rejecting the null hypothesis when it is false.

(iii) For a 2-sided test with a 5% significance level, 2.5% of the total distribution will be in each tail rejection region.

(iv) This statement is incorrect because for a 2-sided test with a 5% significance level, only 2.5% of the total distribution will be in each tail, not 5%.

Therefore, the correct answer is B. (i) and (iii) only.

gpto1