Which statement is correct concerning the decomposition of the total variation?
A) By comparing the Y variance estimates based on between-group and within group variation,we can test the null hypothesis.
B) If the population mean is the same in all the groups,then the variation in the sample means and the sizes of the sample groups can be used to estimate the variance of Y.
C) Because it is not known that all the groups have the same mean,we cannot calculate the variance of all the observations together.
D) All statements are correct.

Question

Quizplus · Accepted Answer

All statements are correct. The decomposition of the total variation allows us to test the null hypothesis by comparing the variance estimates based on between-group and within-group variation. If the population mean is the same in all the groups, then the variation in the sample means and the sizes of the sample groups can be used to estimate the variance of Y. Because it is not known that all the groups have the same mean, we cannot calculate the variance of all the observations together.

Which Statement Is Correct Concerning the Decomposition of the Total