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粗眉毛辣椒油 · 2024年01月21日

求样本均值的标准误计算公式为什么不是标准差/200开根号，而要用置信区间均值+1.96倍标准差呢

  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

置信区间求得的标准差，再除以根号下200，这样为什么不对？

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1 个答案

品职答疑小助手雍 · 2024年01月21日

同学你好，你说的是那标准差正着算均值标准误的情况，是需要除以根号n的。

这题是倒着算的情况，也就是已经知道了使用标准误计算出来的interval了，倒着求标准误，那就不用再除了，倒着算出来就是标准误了。

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