A选项为啥错，C选项为啥对

NO.PZ2015120604000146

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：

It is appropriate to use the F-test.

The hypothesis is : $H_{0} : σ^{2} \leq 3.24 %.$

It is appropraite to use the chi-square test.

解释：

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

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

题干问选择least appropriate,So choose A.

X²是检验一个总体的方差的，题目中bondA和bondB是检验两个总体方差，为什么用F分布是不对的呢？错三次了，就是整不明白

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星星_品职助教 · 2022年03月17日

同学你好，

这道题要检查的是“whether the variance of bond A is greater than 3.24%”，这是在检验A的方差是不是等于一个确定的数字3.24%，所以应该用卡方检验。

如果题目还要检验B的方差是否也等于一个确定的数，那还是应该应用卡方检验。

只有在检验 A的方差是不是等于/大于等于/小于等于 B的方差时，才是两个方差之间的比较，此时才要用到F检验。

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