问题


There is a single choice question about high school statistics. Answer the question by replying A, B, C or D.
Question: The Department of Health plans to test the lead level in a specific park. Because a high lead level is harmful to children, the park will be closed if the lead level exceeds the allowed limit. The department randomly selects several locations in the park, gets soil samples from those locations, and tests the samples for their lead levels. Which of the following decisions would result from the type I error?
A. Closing the park when the lead levels are within the allowed limit
B. Keeping the park open when the lead levels are in excess of the allowed limit
C. Closing the park when the lead levels are in excess of the allowed limit
D. Keeping the park open when the lead levels are within the allowed limit
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

A.
A
deepseekr1

The question involves identifying the decision resulting from a Type I error in hypothesis testing. A Type I error occurs when the null hypothesis is incorrectly rejected when it is actually true. In this scenario, the null hypothesis (H₀) is that the park's lead levels are within the allowed limit (safe), and the alternative hypothesis (H₁) is that lead levels exceed the limit (unsafe).

A Type I error would mean closing the park (rejecting H₀) even though the lead levels are actually safe (H₀ is true). This corresponds to **Option A**.

- **Option B** describes a Type II error (failing to reject a false H₀).
- **Options C and D** represent correct decisions (closing when unsafe or keeping open when safe).

**Answer:** A
A
gpto1 A A
GPT-4o A. Closing the park when the lead levels are within the allowed limit A
llama3.1-70B-Instruct

A
A
llama3.1-405B-Instruct

A
A
DeepSeek-Coder-V2 A. Closing the park when the lead levels are within the allowed limit A
Qwen2-72B-Instruct A. Closing the park when the lead levels are within the allowed limit A
baichuan4 A. Closing the park when the lead levels are within the allowed limit A
doubao A

A type I error is when a true null hypothesis is rejected. In this case, the null hypothesis is that the lead levels are within the allowed limit. Closing the park when the lead levels are actually within the allowed limit is a type I error.
A
minimax A. Closing the park when the lead levels are within the allowed limit A
kimi A. Closing the park when the lead levels are within the allowed limit A
wenxinyiyan A

Explanation:

In statistics, a type I error (also known as a false positive) occurs when a test incorrectly rejects a null hypothesis that is actually true. In this context, the null hypothesis would be that the park's lead levels are within the allowed limit (i.e., the park is safe).

A type I error in this situation would be to incorrectly reject this null hypothesis—that is, to close the park even when its lead levels are actually within the allowed limit. This corresponds to option A.

Option B represents a type II error (also known as a false negative), where the test fails to reject a null hypothesis that is actually false (i.e., keeping the park open when the lead levels are in excess of the allowed limit).

Options C and D represent correct decisions: closing the park when the lead levels are in excess of the allowed limit (C) and keeping the park open when the lead levels are within the allowed limit (D).
A
zhipu A. Closing the park when the lead levels are within the allowed limit

A Type I error occurs when the null hypothesis is true, but it is incorrectly rejected. In this context, the null hypothesis (H0) is that the lead levels are within the allowed limit. If the department incorrectly concludes that the lead levels exceed the allowed limit (rejecting H0 when it is true), they would close the park unnecessarily. This corresponds to option A.
A
gpto1 A A
deepseekv3 The correct answer is:

**A. Closing the park when the lead levels are within the allowed limit**

### Explanation:
A **Type I error** occurs when the null hypothesis is rejected when it is actually true. In this context:
- The null hypothesis is that the lead levels are within the allowed limit.
- Rejecting the null hypothesis means deciding to close the park.

Thus, a Type I error would occur if the park is closed even though the lead levels are within the allowed limit.
A