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Cooljas · 2022年05月23日

为什么算出样本标准差后，不需要除以根号下200呢？公式里不是要除的吗？

  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



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1 个答案

DD仔_品职助教 · 2022年05月24日

嗨，从没放弃的小努力你好：


因为题目让我们求的是标准误standard error，不是标准差，所以的出来的数据直接就是σ/根号下n，不需要再除。

如果求标准差需要把求出的值×根号下200折算成标准差。

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