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许诺 · 2022年06月21日

z统计量与关键值的对比

  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%.

谢谢老师解答！

本题计算出的z-statistic就约为2.58，单尾0.5%的显著性水平对应的关键值也为2.58，检测值就相当于是落在了关键值上。原题问的是大于的情况，在0.5%的显著性水平下，不就属于not to reject H0的情况吗？如果选B，是不是更合理一些？

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星星_品职助教 · 2022年06月21日

同学你好，

本题并不涉及是否拒绝原假设。

题目问的是大于12.32%的概率是多少。由于进行正态分布标准化后，题目可转化为问大于2.58的概率是多少，2.58对应0.5%的面积，即选择A。

对于连续型的正态分布而言，单点的概率为0，所以求P(Z＞2.58)和P(Z≥2.58)的结果是一样的。

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