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Austinzzz · 2021年12月14日

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

  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。

这一个是怎么求出来的，谢谢

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星星_品职助教 · 2021年12月14日

同学你好，

critical value不是求出来的，而是查表得到的。

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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