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xiao15 · 2021年11月08日

有问题

  1. CFA I
  2. Quantitative

NO.PZ2015120604000178

问题如下：

BIM is a well-developed public company and its market capitalization growth rates over past few decades are normally distributed.The population has a mean of 10% and a standard deviation of 5.4%. An investor wants to figure out the probability that BIM's average capitalization growth rate will over 12.32% in the next three years (all the data are monthly statistics).Which of the following option is most accurate?

选项：

A.

0.5%.

B.

1%.

C.

5%.

解释：

A is correct.

It is appropriate to use the central limit theroy to calculate. Standard error=5.4%/36\sqrt {\rm{36}} P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponding probability is 0.5%.

老师有个问题 到底什么时候该用standard erro 什么时候不用 有点搞不清楚 能详细讲一下吗 谢谢

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2 个答案

星星_品职助教 · 2021年12月26日

@姑姑我是你的过儿

这是涉及到数学证明：只有当分母为n-1时，样本标准差才是总体标准差的无偏估计量。

类似的证明CFA里都是不讲的，了解一下即可。样本标准差的公式基本只考计算。

星星_品职助教 · 2021年11月08日

同学你好，

①standard error是样本统计量的标准差。一般有几个应用场景：

1）考察中心极限定理和标准误本身的公式计算：例如计算sample mean的标准差就需要用σ除以根号n。如果题目中出现了中心极限定理，或者告诉你sample size有多大，大部分都是计算标准误的。

2)对于计算置信区间，或者假设检验时涉及的"样本均值的标准差"同样是标准误的概念

置信区间：

假设检验中的检验统计量：

②sample standard deviation是样本标准差的概念。如果给一组数字，直接让算标准差，就要用分母除以n-1的那个公式来计算。

稳如泰山 · 2021年12月26日

老师，那为什么除以n-1可以更贴近总体标准差呢？

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