F分部里面的S1 S2的平方就是样本的方差是不，就算sample size的n不一样也是？-有问必答-品职教育专注CFA ESG FRM CPA 考研等财经培训课程

F分部里面的S1 S2的平方就是样本的方差是不，就算sample size的n不一样也是？

NO.PZ2022071202000093

问题如下：

Question

The samples are drawn independently and both populations are assumed to be normally distributed

Using the above data, an analyst is trying to test the null hypothesis that the population variances are equal (H₀: $σ_{1}^{2} = σ_{2}^{2}$ ) against the alternative hypothesis that the variances are not equal (H_a: $σ_{1}^{2} \neq σ_{2}^{2}$ ) at the 5% level of significance. The table of the F-distribution is provided below.

Table

of the F-Distribution

Which of the following statements is most appropriate? The critical value is:

选项：

A.6.39 and reject the null. B.9.60 and do not reject the null. C.7.15 and do not reject the null.

解释：

Solution

B is correct. The test statistic makes use of the F-distribution and is the ratio of the variances, with the larger variance in the numerator. The test statistic is $F = s_{2}^{2} / s_{1}^{2}$ = 28/4 = 7. The degrees of freedom are 4 by 4. As it is a two-tailed test, the correct critical value at α = 5% is 9.60 (Panel B). As the test statistic is less than the critical value (i.e., 7 < 9.60), the null hypothesis cannot be rejected.

A is incorrect. It uses 4 by 4 degrees of freedom and does not divide the given alpha by two as is appropriate for a two-tailed test.

C is incorrect. It uses the 5 by 5 critical value (i.e., 5 degrees of freedom) rather than correctly using the 4 by 4 value (i.e., 4 degrees of freedom).

F分部里面的S1 S2的平方就是样本的方差是不，就算sample size的n不一样也是？

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