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.