In an analysis of variance,if the null hypothesis is false,then
A)the variation between sample means reflects the variation within the populations as well as the variation between the population means.
B)the within-groups variance is significantly larger than the between-groups variance.
C)the variance within each sample is larger than if the null hypothesis were true.
D)the variance between sample means is no greater than the variance within the population with the largest variance.

Question

Quizplus · Accepted Answer

If the null hypothesis is false, it means that at least one of the population means being compared is significantly different from the others. This difference will be reflected in the between-groups variation. However, it will also affect the within-groups variation as the groups will no longer be comparable. Therefore, the variation between sample means reflects the variation within the populations as well as the variation between the population means.

In an Analysis of Variance,if the Null Hypothesis Is False,then