The correct null ($H_0$) and alternative ($H_a$) hypothesis for a One-Way ANOVA is:

Null Hypothesis ($H_0$): $\mu_1 = \mu_2 = \mu_3 = \ldots = \mu_k$ (All group means are equal)
Alternative Hypothesis ($H_a$): At least one of the group means is not equal to the others.

Thus, the correct choice is:
$H_0: \mu_1 = \mu_2 = \mu_3 = \ldots = \mu_k$
$H_a: \text{At least one of the group means is not equal}$

Explanation:

• Null Hypothesis ($H_0$) assumes that there is no difference in the group means across all groups.
• Alternative Hypothesis ($H_a$) states that at least one group mean differs, indicating that not all means are equal.

Common Misconceptions:

• The alternative hypothesis does not require specifying how many means are different, only that at least one is.
• This test compares group means ($\mu$) and not proportions ($p$).

---

Do you want more details or have any questions about this topic?

Related Questions:

1. How does the F-test determine whether to reject the null hypothesis in ANOVA?
2. What assumptions must be met to perform a One-Way ANOVA?
3. How is the test statistic for a One-Way ANOVA calculated?
4. What is the difference between One-Way ANOVA and Two-Way ANOVA?
5. How do post-hoc tests (e.g., Tukey's HSD) help in ANOVA analysis?

Tip:

Before performing ANOVA, ensure that the assumptions of normality and homogeneity of variance are satisfied for accurate results.