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摩羯大小姐 · 2022年01月22日

为什么要除以2，大于有个数不是单边检验直接用1%就可以吗

  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%.

从哪里看出来是双边检验的？
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已采纳答案

星星_品职助教 · 2022年01月23日

@摩羯大小姐

假设检验要设置原假设和备择假设。此后给出置信度（例如5% significance level），得到拒绝或者不能拒绝原假设的结果。如果这道题在以上的几个方向上出题，就是考察假设检验。

但这道题没有在这方面设置考点，只是要求计算正态分布下X大于12.32%的概率。这是正态分布标准化的考点，根据公式直接做标准化后查表（本题是直接用背诵值）就可以得到结果。整道题没有去“test”任何的东西。

星星_品职助教 · 2022年01月23日

@ 摩羯大小姐

已经回复：本题不涉及任何单边或双边检验，不存在one tailed test。

通过±2.58对应99%置信区间可知，左右侧尾部的总面积为1%，根据对称性，得到右侧尾部面积为0.5%。

摩羯大小姐 · 2022年01月23日

我没明白为啥不是单边检验。不是看是否大于一个值吗？

星星_品职助教 · 2022年01月22日

同学你好，

本题不涉及单边或双边检验。

本题的考察点为正态分布标准化，将题干中信息​P(X＞12.32%)标准化后得到：P(Z＞2.58)，也就是求2.58这个值右侧的面积。

由于±2.58对应99%置信区间，根据对称性可知，﹢2.58右侧对应的面积是1-99%即1%的一半，即0.5%。



摩羯大小姐 · 2022年01月23日

明白P(Z＞2.58)，要求2.58这个值右侧的面积。 由于±2.58对应99%置信区间，就以右边1%为节点就可以了，所以是个one tailed test。为什么要考虑对称性呢？

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