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差不多小姐 · 2021年04月23日

这个为什么不是使用单尾检验?

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%.

如果是单尾检验,那应该就是1%呀 为什么不使用单尾呢

3 个答案

星星_品职助教 · 2021年04月23日

@差不多小姐

只有在涉及假设检验的时候才会有单尾/双尾检验。单双尾的选择看备择假设。

但这道题和假设检验没有关系,没法展开讲解,题库里假设检验的题目很多,如果做到了有疑问可以继续提问~


差不多小姐 · 2021年04月23日

那什么时候使用单尾什么时候使用双尾呢

星星_品职助教 · 2021年04月23日

同学你好,

这道题并没有考察假设检验。

本题是正态分布标准化的考点。题目要计算的P(X>12.32%)通过正态分布标准化的公式转化后,可得到要求的是P(Z>2.58).

标准正态分布下,2.58所对应的左尾面积为99.5%,可直接得到右尾即为0.5%。

这个结果可以根据上课要求背诵的(正态分布下)99%的置信区间对应的关键值为2.58这个结论直接得到。99%置信区间即说明两侧尾部面积都各自分别为0.5%。

也可以通过查表验证这个结果。

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