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银色羽毛 · 2023年08月09日

什么时候用标准误什么时候用标准差

  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


我可能公式有点搞混了，请问置信区间的计算什么时候使用 平均值+z×标准差，什么时候使用平均值+z×标准误

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1 个答案

星星_品职助教 · 2023年08月09日

同学你好，

一个简单的判断准则是看这个置信区间是针对谁的。

如果针对的是样本均值X bar，那么后面的标准差就是X bar的标准差，样本统计量的标准差就是标准误。绝大多数情况都是这种类型。

如果针对的是总体均值μ，那么后面就是总体标准差σ。这种情况的题目较少。

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