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Victoriazhang · 2021年09月08日

这道题目能详细讲一下么

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: 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.

没有特别明白怎么算的 还有表可以提供下么

1 个答案
已采纳答案

星星_品职助教 · 2021年09月09日

同学你好,

卡方统计量的计算公式如下:

代入n=25,S^2= 0.013924,σ0的平方=0.0144,可以求得卡方统计量为23.2067。进而和查表所得的关键值对比即可。

这个公式考纲上没有明显写明要求计算,但20年的Mock出现了一道计算题,所以也需要掌握一下。

卡方分布表目前没有提供下载,可以去原版书的附录里查一下。

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