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Hsuyachien · 2022年11月24日

原假设应该什么样的？

  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。

老师，这个原假设应该是H0:方差≠0.0144，还是=0.0144？因为他想要的=0.0144，所以要放在Ha=0.0144对吧。

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星星_品职助教 · 2022年11月24日

同学你好，

只要检验是否等于一个确定的数字，原假设一定是等于这个数字，也就是=0.0144。相应的备择假设就是不等于这个数字。

只有涉及到检验大于或者小于这种关系时，才会考虑“想要证明的放备择假设”

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