What conditions are necessary in order to use a one-way ANOVA test? Which conditions below are necessary? Select all that apply. $$ \square $$ A. The sample must be randomly selected from the same population. $$ \square $$ B. The sample sizes must be equal. $$ \square $$ C. Each population must have the same variance. $$ \square $$ D. The samples must be randomly selected from a normal, or approximately normal, population. $$ \square $$ E. There must be at least 3 samples. $$ \square $$ F. The samples must be independent of each other.

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To determine the necessary conditions for using a one-way ANOVA test, let's analyze each option provided:

1. **A. The sample must be randomly selected from the same population.**
   - This statement is not entirely accurate. In a one-way ANOVA, we compare means from different groups (populations), so the samples should be randomly selected from different populations, not the same one.

2. **B. The sample sizes must be equal.**
   - This is not a strict requirement. While equal sample sizes can improve the robustness of the ANOVA, it is not necessary for the test to be valid. ANOVA can be performed with unequal sample sizes.

3. **C. Each population must have the same variance.**
   - This is a necessary condition. One of the assumptions of ANOVA is that the variances of the populations being compared are equal (homogeneity of variance).

4. **D. The samples must be randomly selected from a normal, or approximately normal, population.**
   - This is also a necessary condition. ANOVA assumes that the data in each group are normally distributed, especially important when sample sizes are small.

5. **E. There must be at least 3 samples.**
   - This is a necessary condition. One-way ANOVA requires at least three groups to compare their means.

6. **F. The samples must be independent of each other.**
   - This is a necessary condition. The samples must be independent for the ANOVA test to be valid.

Based on this analysis, the necessary conditions for using a one-way ANOVA test are:

- **C. Each population must have the same variance.**
- **D. The samples must be randomly selected from a normal, or approximately normal, population.**
- **E. There must be at least 3 samples.**
- **F. The samples must be independent of each other.**

Thus, the correct selections are C, D, E, and F.
The necessary conditions for using a one-way ANOVA are: - Each population must have the same variance (C). - Samples must be randomly selected from a normal, or approximately normal, population (D). - There must be at least 3 samples (E). - Samples must be independent of each other (F).

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