问题


There is a single choice question about high school statistics. Answer the question by replying A, B, C or D.
Question: After receiving several complaints from his customers about the store being closed on Sundays, a storekeeper decided to conduct a survey. He randomly selected 100 female customers and 120 male customers, and asked them, "Are you interested in shopping at this store on Sundays?" He counted the number of customers answering "yes" and constructed a 95 percent confidence interval for the difference by subtracting the proportions of female from the proportion of male customers in favor of shopping on Sundays. The resulting interval was (–0.23, –0.18). Which of the following is a correct interpretation of the interval?
A. We are 95 percent confident that the proportion of women interested in shopping on Sundays exceeds the proportion of men interested in shopping on Sundays.
B. We are 95 percent confident that the proportion of men interested in shopping on Sundays exceeds the proportion of women interested in shopping on Sundays.
C. We are 95 percent confident that the proportion of women interested in shopping on Sundays is equal to the proportion of men interested in shopping on Sundays.
D. Because the interval contains negative values, it is invalid and should not be interpreted.
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

B. We are 95 percent confident that the proportion of men interested in shopping on Sundays exceeds the proportion of women interested in shopping on Sundays.		 A
deepseekr1

The confidence interval was constructed by subtracting the proportion of female customers from the proportion of male customers (p_male - p_female). The interval (–0.23, –0.18) is entirely negative, indicating that p_male is less than p_female. This means the proportion of women interested in shopping on Sundays is higher than that of men. The interval does not include zero, ruling out equality (Option C). Negative values in the interval are valid and reflect the direction of the difference, so Option D is incorrect. Option B incorrectly states that men's proportion exceeds women's.

**Answer:** A		 A
gpto1 A A
GPT-4o B. We are 95 percent confident that the proportion of men interested in shopping on Sundays exceeds the proportion of women interested in shopping on Sundays. A
llama3.1-70B-Instruct

B		 A
llama3.1-405B-Instruct

A.

The interval (–0.23, –0.18) does not contain 0, so the null hypothesis that the proportion of women interested in shopping on Sundays is equal to the proportion of men interested in shopping on Sundays can be rejected. Since the interval contains only negative values, the proportion of women interested in shopping on Sundays is greater than the proportion of men interested in shopping on Sundays.		 A
DeepSeek-Coder-V2 B A
Qwen2-72B-Instruct B. We are 95 percent confident that the proportion of men interested in shopping on Sundays exceeds the proportion of women interested in shopping on Sundays. A
baichuan4 B A
doubao B

The interval (–0.23, –0.18) indicates that the lower bound and upper bound are both negative, meaning the proportion of male customers interested in shopping on Sundays is likely to be greater than the proportion of female customers interested in shopping on Sundays with 95% confidence.		 A
minimax A. We are 95 percent confident that the proportion of women interested in shopping on Sundays exceeds the proportion of men interested in shopping on Sundays. A
kimi A. We are 95 percent confident that the proportion of women interested in shopping on Sundays exceeds the proportion of men interested in shopping on Sundays.

The confidence interval is (–0.23, –0.18), which means that the difference between the proportion of female and male customers who are interested in shopping on Sundays is negative. Since the interval does not include zero, we can be 95% confident that the proportion of women interested is greater than the proportion of men.		 A
wenxinyiyan B

Explanation:

The confidence interval given is (–0.23, –0.18). This interval represents the difference between the proportions of male and female customers who are interested in shopping on Sundays, with the proportion of male customers subtracted from the proportion of female customers.

Since the entire interval lies below zero, it indicates that the proportion of male customers interested in shopping on Sundays is higher than the proportion of female customers. In other words, the proportion of men interested exceeds the proportion of women.

Therefore, option B is correct: "We are 95 percent confident that the proportion of men interested in shopping on Sundays exceeds the proportion of women interested in shopping on Sundays."		 A
zhipu B. We are 95 percent confident that the proportion of men interested in shopping on Sundays exceeds the proportion of women interested in shopping on Sundays.

Explanation: The confidence interval (–0.23, –0.18) represents the difference between the proportion of male customers and the proportion of female customers who are interested in shopping on Sundays. Since the interval is entirely negative, it indicates that the proportion of male customers who are interested in shopping on Sundays is higher than the proportion of female customers by an amount that falls between 0.18 and 0.23. Therefore, the correct interpretation is that we are 95 percent confident that the proportion of men interested in shopping on Sundays exceeds the proportion of women interested in shopping on Sundays.		 A
gpto1 A A
deepseekv3 The 95% confidence interval for the difference in proportions (male minus female) is (–0.23, –0.18). Since the entire interval is negative, it indicates that the proportion of men interested in shopping on Sundays is less than the proportion of women interested in shopping on Sundays. Therefore, the correct interpretation is:

**A. We are 95 percent confident that the proportion of women interested in shopping on Sundays exceeds the proportion of men interested in shopping on Sundays.**

Answer: **A**		 A