金声玉亮2.0模型评测报告

问题

There is a single choice question about high school statistics. Answer the question by replying A, B, C or D.
Question: The president of an online music streaming service whose customers pay a fee wants to gather additional information about customers who have joined in the past 12 months. The company plans to send out an e-mail survey to a sample of current customers with a link that gives participants a month of streaming service for free once the survey has been completed. They know that musical tastes vary by geographical region. Which of the following sample plans would produce the most representative sample of its customers?
A. Choose all of the customers who joined in the last month.
B. Make a list of all the customers who joined in the last 12 months and choose a random sample of customers on this list.
C. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 10 customers from each state.
D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.
Answer:

答案

模型	模型答案	正确答案
金声玉亮2.0	D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.	D
deepseekr1	The question focuses on selecting the most representative sample of customers who joined in the past 12 months, considering that musical tastes vary by geographical region. Here's the analysis of the options: - Option A selects only customers from the last month, which ignores the full 12-month period and likely underrepresents regional diversity over time. - Option B uses a simple random sample but does not guarantee proportional representation of states, risking over- or underrepresentation of certain regions. - Option C takes 10 customers per state, which overrepresents smaller states and underrepresents larger ones (e.g., 10 from a state with 100 customers vs. 10,000). - Option D selects 3% of customers from each state, ensuring that each state’s contribution to the sample is proportional to its actual customer base. This maintains regional diversity and aligns with the need to account for geographical variation in musical tastes. Answer: D	D
gpto1	D	D
GPT-4o	D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.	D
llama3.1-70B-Instruct	D	D
llama3.1-405B-Instruct	D. The sample should be selected in a way that allows all of the customers to be equally likely to be selected. In this case, the sample should be stratified by state to ensure that the number selected is proportional to the number of customers in each state. Choice (A) will not give a representative sample of all of the customers who joined in the last 12 months. Choice (B) may give a sample that is too large and may not be allowed with the condition of the problem. Choice (C) may not give a representative sample because each state has a different number of customers. The best answer is D.	D
DeepSeek-Coder-V2	D	D
Qwen2-72B-Instruct	D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.	D
baichuan4	D	D
doubao	D Sampling a fixed percentage from each state (as in option D) takes into account the variation in musical tastes by geographical region and is likely to give a more representative sample compared to the other options. Option A only focuses on the most recent month's customers and may not represent the entire 12-month period. Option B is a random sample but doesn't consider the geographical variation. Option C may not be as representative if the number of customers in each state is very different.	D
minimax	B. Make a list of all the customers who joined in the last 12 months and choose a random sample of customers on this list.	D
kimi	D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state. This option ensures that the sample is representative of the entire customer base by taking into account the geographical variation in musical tastes. By selecting a consistent percentage from each state, the sample will be more likely to reflect the overall distribution of customers across different regions.	D
wenxinyiyan	D	D
zhipu	D Explanation: To ensure the sample is representative of the overall customer base, it's important to account for the geographical variation in musical tastes. While options B and C also consider the entire customer base over the past 12 months, option D provides a proportional representation by choosing a percentage (3%) of customers from each state. This approach ensures that the sample size from each state is proportional to the number of customers in that state, making the sample more representative of the entire customer base than choosing a fixed number (like 10) from each state, which might overrepresent or underrepresent certain states depending on their customer population. Option A is not representative as it only includes customers from the last month, which may not reflect the broader trends over the past 12 months.	D
gpto1	D	D
deepseekv3	D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state. This method is the most representative because it accounts for geographical variation in musical tastes by ensuring that each state is proportionally represented in the sample. By selecting 3% of customers from each state, the sample will reflect the distribution of customers across different regions, providing a more accurate and representative picture of the overall customer base.	D

模型

模型答案

正确答案

金声玉亮2.0

D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.

deepseekr1

The question focuses on selecting the most representative sample of customers who joined in the past 12 months, considering that musical tastes vary by geographical region. Here's the analysis of the options:

- **Option A** selects only customers from the last month, which ignores the full 12-month period and likely underrepresents regional diversity over time.
- **Option B** uses a simple random sample but does not guarantee proportional representation of states, risking over- or underrepresentation of certain regions.
- **Option C** takes 10 customers per state, which overrepresents smaller states and underrepresents larger ones (e.g., 10 from a state with 100 customers vs. 10,000).
- **Option D** selects 3% of customers from each state, ensuring that each state’s contribution to the sample is proportional to its actual customer base. This maintains regional diversity and aligns with the need to account for geographical variation in musical tastes.

**Answer: D**

gpto1

GPT-4o

D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.

llama3.1-70B-Instruct

llama3.1-405B-Instruct

D. The sample should be selected in a way that allows all of the customers to be equally likely to be selected. In this case, the sample should be stratified by state to ensure that the number selected is proportional to the number of customers in each state. Choice (A) will not give a representative sample of all of the customers who joined in the last 12 months. Choice (B) may give a sample that is too large and may not be allowed with the condition of the problem. Choice (C) may not give a representative sample because each state has a different number of customers.
The best answer is D.

DeepSeek-Coder-V2

Qwen2-72B-Instruct

D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.

baichuan4

doubao

D

Sampling a fixed percentage from each state (as in option D) takes into account the variation in musical tastes by geographical region and is likely to give a more representative sample compared to the other options. Option A only focuses on the most recent month's customers and may not represent the entire 12-month period. Option B is a random sample but doesn't consider the geographical variation. Option C may not be as representative if the number of customers in each state is very different.

minimax

B. Make a list of all the customers who joined in the last 12 months and choose a random sample of customers on this list.

kimi

D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.

This option ensures that the sample is representative of the entire customer base by taking into account the geographical variation in musical tastes. By selecting a consistent percentage from each state, the sample will be more likely to reflect the overall distribution of customers across different regions.

wenxinyiyan

zhipu

D

Explanation: To ensure the sample is representative of the overall customer base, it's important to account for the geographical variation in musical tastes. While options B and C also consider the entire customer base over the past 12 months, option D provides a proportional representation by choosing a percentage (3%) of customers from each state. This approach ensures that the sample size from each state is proportional to the number of customers in that state, making the sample more representative of the entire customer base than choosing a fixed number (like 10) from each state, which might overrepresent or underrepresent certain states depending on their customer population. Option A is not representative as it only includes customers from the last month, which may not reflect the broader trends over the past 12 months.

gpto1

deepseekv3

D. From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.

This method is the most representative because it accounts for geographical variation in musical tastes by ensuring that each state is proportionally represented in the sample. By selecting 3% of customers from each state, the sample will reflect the distribution of customers across different regions, providing a more accurate and representative picture of the overall customer base.