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iamjj · 2022年12月06日

为什么算出来的数不用再除以根号100？

  1. CFA I
  2. Quantitative

NO.PZ2015120604000125

问题如下：

The population is 6000 programmer which is supposed to be normally distributed. A sample with 100 size is drawn from the population. Based on z-statistic, 95% confidence interval of sample mean of annual salary is 32.5 (in thousands) dollars ranges from 22 (in thousands) dollars to 43 (in thousands) dollars .Calculate the standard error of mean annual salary:

选项：

A.

1.96.

B.

3.99.

C.

5.36.

解释：

C is correct.

At the 95% level of significance, the critical value is ±1.96.

So the confidence interval is 32.5±1.96 σ x ¯ ,

From the equation t 32.5 + 1.96 standard error = 43 or 32.5 - 1.96 standard error x ¯ = 22, we get σ x ¯ =5.36.=5.3571.


根据题干的sample mean=32.5，基于z-statistics的95%的置信区间（得到关键值±1.96），和置信区间的公式，可以得到 32.5 + 1.96 standard error = 43 或 32.5 - 1.96 standard error = 22。

得到 standard error=5.3571


按照1.96个标准差=43-32.5=10.5

可以算出标准差等于5.35，但是这个不是样本的标准差吗，为什么不需要再除以一个根号100，得到standard error呢

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1 个答案

星星_品职助教 · 2022年12月06日

同学你好，

围绕样本均值的置信区间中，对应的标准差也为样本均值的标准差，即标准误。standard error=σ/根号n。

所以，通过置信区间公式直接计算出来的就是standard error，即计算出来的结果就已经是σ/根号n，不需要再额外去除以一个根号n了。

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