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Eddie · 2023年02月21日

请问significant level 是5%，对应的critical value 不应该是1.96，为什么是1.65？

  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 approptiate 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.

如题

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1 个答案

星星_品职助教 · 2023年02月21日

同学你好，

课上要求背诵的关键值基于的都是置信区间，如90%置信区间对应关键值为±1.65。对于此置信区间而言，两侧的尾部总面积为10%，单侧尾部面积为5%。

即±1.65是单侧尾部5%所对应的关键值。

回到本题，根据题干描述“...the mean of bond B is greater than 26%”，可知备择假设为μ＞26%。也就说明这是一个单尾检验，significant level=5%对应就是单尾的面积为5%。

所以，关键值也和90%的置信区间一样为±1.65；

-------

与此对比，95%置信区间的关键值±1.96对应的是单侧尾部为2.5%的情况，并不是单尾面积5%。

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