问题


There is a single choice question about high school statistics. Answer the question by replying A, B, C or D.
Question: Fifty oranges of one variety were selected at random and weighed. A 95 percent confidence interval computed from the sample weights to estimate the mean weight of oranges of this variety is (7.58, 8.72) ounces. Which of the following statements is true with respect to the confidence level used?
A. In repeated samplings of the same size, 95 percent of the intervals constructed will contain the true mean weight of the oranges of this variety.
B. In repeated samplings of the same size, 95 percent of the intervals constructed will contain the sampled mean weight of the oranges.
C. Ninety-five percent of the oranges in this sample weigh between 7.58 and 8.72 ounces.
D. Ninety-five percent of the oranges of this variety weigh between 7.58 and 8.72 ounces.
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

A.		 A
deepseekr1

Answer: A

**Explanation:**
A confidence interval provides a range of plausible values for a population parameter (here, the true mean weight). The 95% confidence level means that if we were to take many random samples of the same size and compute a confidence interval for each, approximately 95% of these intervals would contain the true population mean.

- **Option A** correctly states this interpretation.
- **Option B** incorrectly claims the intervals contain the "sampled mean" (a specific sample statistic) instead of the true population mean.
- **Options C and D** incorrectly apply the interval to individual oranges, not the mean. Confidence intervals do not describe the range of individual data points.

Thus, the correct answer is **A**.		 A
gpto1 A A
GPT-4o A. In repeated samplings of the same size, 95 percent of the intervals constructed will contain the true mean weight of the oranges of this variety. A
llama3.1-70B-Instruct

A		 A
llama3.1-405B-Instruct

A. In repeated samplings of the same size, 95 percent of the intervals constructed will contain the true mean weight of the oranges of this variety.		 A
DeepSeek-Coder-V2 A A
Qwen2-72B-Instruct A. In repeated samplings of the same size, 95 percent of the intervals constructed will contain the true mean weight of the oranges of this variety. A
baichuan4 A A
doubao A A
minimax A. In repeated samplings of the same size, 95 percent of the intervals constructed will contain the true mean weight of the oranges of this variety. A
kimi A. In repeated samplings of the same size, 95 percent of the intervals constructed will contain the true mean weight of the oranges of this variety. A
wenxinyiyan A A
zhipu A

Explanation: A 95 percent confidence interval means that if we were to take many samples of the same size from the population and compute a confidence interval for each sample, approximately 95 percent of those intervals would contain the true population mean. This is precisely what option A describes. The other options are incorrect because:

- B refers to containing the sampled mean, which is not the purpose of a confidence interval.
- C refers to the weights of the oranges in this particular sample, not the population mean.
- D incorrectly suggests that the interval describes the distribution of individual weights in the population, rather than the mean weight.

Therefore, the correct answer is A.		 A
gpto1 A A
deepseekv3 The correct answer is **A**.

**Explanation:**

A 95% confidence interval means that if we were to take many samples of the same size from the population and compute a confidence interval for each sample, then 95% of those intervals would contain the true population mean. This is the correct interpretation of a confidence interval.

The other options are incorrect:

- **B** is incorrect because the confidence interval is about the true population mean, not the sample mean.
- **C** is incorrect because the confidence interval does not describe the range of individual weights in the sample.
- **D** is incorrect because the confidence interval does not describe the range of individual weights in the population.

Thus, the correct answer is **A**.		 A