High School

What conditions must \( n \) satisfy to make the \(\chi^2\) test valid?

A. \( n \) must be equal to 10 or more.

B. \( n \) must be equal to 5 or more.

C. \( n \) must be large enough so that for every cell, the expected cell count will be equal to 10 or more.

D. \( n \) must be large enough so that for every cell, the expected cell count will be equal to 5 or more.

Answer :

For the chi-square (x^2) test to be valid, N must be large enough so that for every cell the expected cell count will be equal to 5 or more.

To make the x^2 test valid, N must be large enough so that for every cell the expected cell count will be equal to 5 or more. In other words, N must be such that each cell in the contingency table has a sufficient number of observations to ensure that the test is reliable. Some guidelines suggest that N should be at least 10 or more, while others suggest that N should be at least 5 or more. However, the most important consideration is to ensure that the expected cell count is not too low, as this can lead to inaccurate or misleading results. Therefore, the key condition for a valid x^2 test is to have a sufficiently large sample size to ensure that each cell has an expected count of at least 5.

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