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欢欢 · 2021年08月18日

99％对应的cv不是2.58吗？

  1. CFA I
  2. Quantitative

NO.PZ2015120604000131

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

99％对应的cv不是2.58吗？
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星星_品职助教 · 2021年08月19日

同学你好，

“A one-tailed test with a significance level of 1% ...”说明是单尾的面积就是1%。这个对应的关键值是2.33。建议也记一下，二级还会用到。

而±2.58是正态分布下99%置信区间的关键值，对应的是双尾总面积为1%，也等价于单尾面积为0.5%.


欢欢 · 2021年08月20日

好的谢谢。那我可不可以理解为，对于置信度是98％的双尾z分布，它的置信区间就是（-2.33，2.33）

星星_品职助教 · 2021年08月20日

@欢欢

理解基本是对的。规范的说法是：对于正态分布下置信度为98%的置信区间，或significance level为2%的双尾检验，对应的关键值为±2.33.

但考试从没有从双尾98%的角度出过题。所以这个点建议掌握的是：正态分布下，（无论是置信区间还是假设检验）总之单尾面积1%对应的关键值（的绝对值）是2.33。这点在一二级的组合里求VaR的时候也会频繁的应用到。

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