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功不唐捐-11 · 2025年06月18日

标准误差为什么没有/根号n?

  1. FRM I
  2. Quantitative

NO.PZ2019040801000025

问题如下：

Assuming the height of a tree in a forest follows a normal distribution, there are more than 10,000 trees. The sample size of test is 200, the 95% confidence interval of the sample mean of the height is 11 to 35 meters based on a z-statistic, the standard error of mean height is closest to:

选项：

A.

1.96.

B.

3.58.

C.

6.12.

D.

10.50.

解释：

C is correct.

考点：The central limit theorem (CLT)

解析：95%的置信区间是11到 35，z值是1.96.

平均数为0.5*（11+35）=23.所以置信区间是23 ± 1.96sx, sx是标准误。23+1.96sx等于35，sx等于6.12米

标准误差为什么没有/根号n?,利用置信区间算出来样本的标准差为6.12，样本总量为200，均值的标准误不应该是6.12/根号200么？期待解答，谢谢

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1 个答案

李坏_品职助教 · 2025年06月18日

嗨，爱思考的PZer你好：


σ或者s除以根号n的那个叫standard error, 也就是标准误。


但是，如果是在置信区间的题目里：

置信区间 = 均值23 ± Z * standard error, 95%置信度的Z是1.96 ，这个是要记住的。

置信区间的上界是35， 35 = 23 + 1.96*standard error，

然后可以求出standard error = 6.12. 这个可以直接求出标准误，就不需要再除以根号n了。

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