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Flying马 · 2024年10月14日

题目一多突然有点恍惚

  1. CFA I
  2. Quantitative

NO.PZ2015120604000147

问题如下：

Here is a table discribing sample statistics from two bonds' rate of return which are both normally distributed over the past decades. If an investor is considering whether the mean of bond B is greater than 26%,

which of the following conclusion is least appropriate (significant level=5%) ?

选项：

A.

It is appropriate to use the Z-test.

B.

The mean of bond B is not significant greater than 26%.

C.

It is a one-tailed test.

解释：

B is correct.

It is appropraite to ues the one-tailed Z-test because the sample size of bond B is bigger than 30.

The null hypothesis is: H0: μ ≤ 26%

The test statistic:


α= 5% indicates the critical value is equal to ±1.65.

Because 1.91>1.65, therefore, we should reject the null hypothesis.

单尾的5% α 是1.65，双尾是1.96  对吗老师

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品职助教_七七 · 2024年10月14日

嗨，爱思考的PZer你好：


单尾的5% α 是1.65，双尾是1.96 对吗----对。


可以直接参考下述总结：

1）数量科目的置信区间都是双尾的，正态分布的前提下，关键值如下：

90%置信区间：±1.645/1.65-----对应单尾面积5%；

95%置信区间：±1.96-------对应单尾面积2.5%；

99%置信区间：±2.58-------对应单尾面积0.5%；

单双尾的面积需要灵活转化，便于对应不同的置信区间/假设检验的考点。

以上值要求背诵。但t分布的关键值只能查表。


2）VaR衡量的是损失，所以只有左侧单尾的情况。

例如5%的VaR（95%置信区间对应的VaR），就相当于左侧单尾为5%，对应上面的“单尾面积5%”，所以关键值就是上面的 -1.645/-1.65

1%的VaR相当于左侧单尾面积1%，这个对应不上，所以需要单独记忆为 -2.33.

绝大多数VaR只会用到这两个值。

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