In the context of ANOVA procedures, what is the null hypothesis?

• A. At least one population mean is different.
• B. $\text{All population means are equal, i.e.,}{\mu }_1={\mu }_2=\dots ={\mu }_k$
• C. The variances of all groups are equal.
• D. The sample means are all different.

Answer: (B)

Verified step by step guidance

1. Understand that ANOVA (Analysis of Variance) is used to compare the means of three or more groups to see if there is evidence that at least one group mean differs from the others.
2. Recall that the null hypothesis in ANOVA always assumes no difference among the group means, meaning all population means are equal.
3. Formally state the null hypothesis as: \(H_0: \mu_1 = \mu_2 = \mu_3 = \dots = \mu_k\), where \(\mu_i\) represents the mean of the \(i^{th}\) group and \(k\) is the number of groups.
4. Recognize that the alternative hypothesis is that at least one population mean is different, but this is not the null hypothesis itself.
5. Therefore, the correct null hypothesis in ANOVA is that all population means are equal.