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Yinghui · 2020年03月08日

问一道题: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 and sample variances are significantly different.

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:   χ 2 = (n1) s 2 σ 0 2 ={(25-1)*0.013924}/0.0144= 23.2067

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.

chi-squared distribution only has one-tailed. 所以为什么不是直接找到df=24, prob=0.05 对应的 entry 36.42, 然后用test statistic 和36.42 比大小就好?

1 个答案

星星_品职助教 · 2020年03月08日

同学你好,

卡方检验的是方差是否等于一个确定的数,所以是一个双尾检验,算出来的test statistics也是对应双尾的,你那种方法对应的是单尾检验,不能混着比较。

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