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ccling · 2020年09月07日

问一道题：NO.PZ2015120604000131 [ CFA I ]

  1. CFA I
  2. Quantitative

问题如下：

Which of the following descriptions is the least accurate about hypothesis testing?

选项：

A.

A Type II error refers to accept the null when it is false.

B.

A one-tailed test with a significance level of 1% has z-critical values of 2.58.

C.

One minus the probability of a Type II error equals the power of test .

解释：

B is correct.

A one-tailed test with a significance level of 1% has z-critical values of 2.33

老师，B选项为什么不对呢？u+_2.58sigma概率是99%啊
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1 个答案

星星_品职助教 · 2020年09月07日

同学你好，

这里的关键词是“one-tailed test ”，单尾检验说明拒绝域只有一侧。而这一侧的面积就已经是1%了。

我们上课背过的是99%的正态分布置信区间对应关键值为2.58，99%置信区间意味着两侧的拒绝域的面积之和是1%，所以根据对称性，单侧拒绝域的面积是0.5%，而不是1%。

所以可以记忆一下，正态分布下单侧0.5%对应的关键值是2.58，但单侧1%对应的关键值是2.33。

2.33这个值在数量里用的非常少，但在组合里算VaR的时候会用到。

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