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凤鸣朝阳兮 · 2020年03月30日

问一道题：NO.PZ2015120604000146

  1. CFA I
  2. Quantitative

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 variance of bond A is greater than 3.24%,

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

选项：

A.

It is appropriate to use the F-test.

B.

The hypothesis is :H0: σ2≤3.24%.

C.

It is appropraite to use the chi-square test.

解释：

A is correct.

The chi-square test is used to test hypotheses concerning a single population variance.

The null hypothesis can place in whatever you want to reject, so B is correct.

卡方检验是检验总体的方差是否等于一个确定的值

本题中说的是检验均值是否大于26%，

因此H0：X均值≤26%，Ha：X均值＞26%

像这种，原假设是小于等于，也算一个确定的值？只要原假设带等于号，就可以用卡方检验？

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1 个答案

星星_品职助教 · 2020年03月30日

同学你好，

无论原假设是“≥”还是“=”还是“≤”，只要是检验方差和一个确定的数的关系，就用卡方检验，不受原假设里的大于小于号影响。

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无论是卡方检验还是均值检验，无论原假设设定为是“≥”还是“=”还是“≤”，检验的其实都是均值/方差等于一个确定的数。所以检验统计量的公式都是一样的。以这道题为例，原假设是H0：σ2≤3.24%，但实际上检验的就是σ2是否等于3.24%，然后根据计算出来的检验统计量和critical value的对比，来确定最终应该是≥3.24%还是＜3.24%。

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