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mayduke · 2022年05月09日

关于查表用的概率值

  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。

critical value是查表得到的。请问为什么查下端点时要用1-0.05/2=0.975的概率？上端点明白。所有自由度➕概率查表的都是按照这个规律吗


根据原版书后的卡方分布表（针对右尾概率），和已知条件1）双尾检验；2）significance level=5%；3）自由度为25-1=24，用概率0.05/2=0.025和自由度24查表得上端点的值为39.36，用1-0.05/2=0.975和自由度24查得下端点为12.4

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1 个答案

星星_品职助教 · 2022年05月10日

同学你好，

原回复里已经解释了这一点，原版书卡方分布表针对的是右尾的概率。

所以一个值要按照右尾概率2.5%查。另一个值要按照左尾概率是2.5%查，但表上只有右尾概率，就需要找到此时右尾的对应概率97.5%后，对应查表。

具体查表规则需要按照具体的分布和原版书对应的表的特点去查。不能一概而论。

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