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南极耳语 · 2023年02月13日

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 (Ha: σ 1 2 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).

1

1 个答案

星星_品职助教 · 2023年02月13日

同学你好,

S1的平方和S2的平方是样本的方差。

如果要去计算样本方差,需要考虑将分母调整为n-1。但由于本题的样本方差已经给出了最终的结果,所以不需要再考虑N了,直接拿这两个数字来用即可。