In the context of an ANOVA (Analysis of Variance) to compare the effectiveness of different treatments for bipolar disorder, the null hypothesis generally states that there is no difference in means between the groups being compared. From the provided options, the two acceptable null hypotheses are:

1. There is no difference between the means of the groups.
2. μ(1) = μ(2) = μ(3)

These hypotheses assert that the means of the symptomatology scores for the three groups (no treatment, psychotherapy, and psychotherapy with medication) are equal, indicating that there is no effect of the treatment on symptomatology.

The other options provided are not appropriate null hypotheses for the following reasons:

• μ(1) - μ(2) - μ(3) = 0: This is not a standard way of expressing a null hypothesis in the context of ANOVA.
• There is at least one group with a different mean: This is actually the alternative hypothesis, which states that there is a significant difference between at least one pair of group means.
• μ(1) = μ(2) = μ(3) = 0: This would imply that the mean symptomatology score for all groups is zero, which is not relevant to the comparison of treatment effects.

Would you like to go into the details of the ANOVA calculation or have any specific questions about this setup?

Here are 5 questions you might ask next:

1. How do you calculate the F-ratio in an ANOVA?
2. What are the assumptions of ANOVA?
3. How do you interpret the results of an ANOVA test?
4. What is the difference between a null hypothesis and an alternative hypothesis?
5. Can you explain how post hoc tests are used following an ANOVA?

Tip: When comparing more than two groups, ANOVA is a powerful statistical method to determine if there are any statistically significant differences among the group means.