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健康菌 · 2022年09月21日

查表significance level的顺序

  1. CFA I
  2. Quantitative

NO.PZ2015120604000144

问题如下：

Quintina conducts a hypothesis to test whether the variance of the annually return is 0.0144. Then she selects a random 25 year's data as a sample, Quintina figures out the variance of the sample is 0.013924. Assume the level of significance is 5%, which of the following conclusion is least accurate?

选项：

A.

The population variance is not significant different from 0.0144.

B.

The population variance is significantly different from 0.0144.

C.

This hypothesis is appropriate to use the chi-square test.

解释：

B is correct.

The null hypothesis is H0: σ2=0.0144. It is appropriate to use the two-tailed chi-square test.

The test statistic is:=(25-1)*0.013924/0.0144=23.21

The critical chi-square critical values are 12.4 and 39.36.

Because the test statistic falls between these two values,so Quintina fails to reject the null hypothesis.

So we conclude that the population variance is not significantly different from 0.0144.

题干是问which is the least accurate?所以选B。

为什么卡方表标题行significance level从大到小？查出来的值在图上是反向关系吗？难道说随着significance level增加，截取的曲线下面积是从右到左？

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1 个答案

星星_品职助教 · 2022年09月22日

同学你好，

这个问题有一些乱，把卡方分布查表的原理和方法具体说一遍，应该就能解决了。

原版书给出的卡方分布表都基于的是右尾面积，所以左侧拒绝域面积2.5%就相当于右尾面积97.5%

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以本题为例，由于是双尾检验，significance level=5%，可知单侧尾部/拒绝域面积为2.5%。

原版书给出的卡方分布表针对的是右尾面积。所以，要查左尾的2.5%，就要去对应表中的（右尾面积）97.5%。

即两个critical value就需要分别对应到表中的右尾0.975和右尾0.025。

根据自由度df=n-1=24，可以得到两个关键值分别为12.401和39.364.


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