Questions: What are the three assumptions that have to be made to use ANOVA? The populations are normally distributed. The populations are independent. The populations have equal standard deviations. One of the sample sizes is larger than the other. The sample size is greater than 6.

Solution Steps

To solve this problem, we need to identify the correct assumptions required to use ANOVA (Analysis of Variance). ANOVA typically requires the following assumptions:

1. The populations are normally distributed.
2. The populations are independent.
3. The populations have equal standard deviations.

To use ANOVA (Analysis of Variance), certain assumptions must be met. These assumptions ensure the validity of the test results. The key assumptions are:

1. The populations are normally distributed: \( \text{Normality} \)
2. The populations are independent: \( \text{Independence} \)
3. The populations have equal standard deviations: \( \sigma_1 = \sigma_2 = \sigma_3 \)

From the provided options, we evaluate which statements align with the assumptions of ANOVA:

• \( \text{A: The populations are normally distributed.} \) (True)
• \( \text{B: The populations are independent.} \) (True)
• \( \text{C: The populations have equal standard deviations.} \) (True)
• \( \text{D: One of the sample sizes is larger than the other.} \) (False)
• \( \text{E: The sample size is greater than 6.} \) (False)

The correct assumptions that must be made to use ANOVA are:

• \( \text{A, B, and C} \)

Final Answer