In a one-way ANOVA, the null hypothesis states that:

In a one-way ANOVA, the null hypothesis states that:

• A. All group means are equal
• B. At least one group mean is different
• C. The variances are equal
• D. The within-group variances are zero

Answer: (A)

One-way ANOVA asks whether several population means are the same. The null hypothesis is that all group means are equal, meaning any differences observed in the sample come from random sampling variability rather than real differences between groups. The test does this by comparing the amount of variation between the group means (between-group variation) to the variation of individual observations within each group (within-group variation). If the between-group variation is small relative to the within-group variation, the F statistic is near 1 and we don’t reject the null. If the between-group variation is large, the F statistic increases, suggesting that at least one group mean differs from the others. This is why the statement that all means are equal is the null. Remember that stating “at least one group mean differs” is the alternative hypothesis, and ANOVA itself doesn’t tell you which groups differ—that requires post hoc tests. Also, assuming equal variances (homogeneity of variances) is an assumption for the validity of the test, not the null itself.

One-way ANOVA asks whether several population means are the same. The null hypothesis is that all group means are equal, meaning any differences observed in the sample come from random sampling variability rather than real differences between groups. The test does this by comparing the amount of variation between the group means (between-group variation) to the variation of individual observations within each group (within-group variation). If the between-group variation is small relative to the within-group variation, the F statistic is near 1 and we don’t reject the null. If the between-group variation is large, the F statistic increases, suggesting that at least one group mean differs from the others. This is why the statement that all means are equal is the null. Remember that stating “at least one group mean differs” is the alternative hypothesis, and ANOVA itself doesn’t tell you which groups differ—that requires post hoc tests. Also, assuming equal variances (homogeneity of variances) is an assumption for the validity of the test, not the null itself.