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The question asks which of the following is **NOT** a requirement for conducting a hypothesis test for independence between row and column variables in a contingency table.

Here are the options:

- **A.** For every cell in the contingency table, the observed frequency \( O \) is at least 5.
- **B.** The sample data are represented as frequency counts in a two-way table.
- **C.** The sample data are randomly selected.
- **D.** For every cell in the contingency table, the expected frequency \( E \) is at least 5.

### Analysis:

- **Option A** is incorrect because the observed frequency does not necessarily have to be at least 5. It is the expected frequency that matters.
- **Option B** is a requirement, as a contingency table is necessary for this type of test.
- **Option C** is correct; sample data must be randomly selected in hypothesis testing.
- **Option D** is correct; one of the key assumptions of the Chi-square test is that the expected frequency \( E \) in each cell should be at least 5 to ensure the test’s validity.

### Conclusion:
The correct answer is **A**, as the observed frequency doesn't need to be at least 5 in every cell, but the expected frequency does.

Would you like more details on this or have any other questions?

Here are 5 relative questions to explore:
1. What is a contingency table and how is it constructed?
2. How does the Chi-square test for independence work?
3. What happens if the expected frequency in some cells is less than 5?
4. How do you calculate expected frequency in a contingency table?
5. What other tests can be used when the assumptions of the Chi-square test are not met?

**Tip:** Always check the assumptions of a statistical test before applying it to ensure the results are valid.

Which of the following is NOT a requirement of conducting a hypothesis test for independence between the row variable and column variable in a contingency table?

Explore the requirements for conducting a hypothesis test for independence between variables in a contingency table using the Chi-square test. This problem focuses on key statistical concepts such as expected frequencies and sample selection criteria.

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