Discussion
The value of \(\chi^{2}\) in a \(3 \times 5\) contingency table is computed as 8.0. The Null hypothesis of no association will be tested at 5% level of significance, if this value is less than or equal to the value of \(\chi^{2}\) from the table at degrees of freedom :
Answer: A
The degrees of freedom of a chi-square test of association in a contingency table with r rows and c columns are:
\[ (r - 1)(c - 1) \]
\[ (3 - 1)(5 - 1) = 8 \]
The key therefore gives 8, the first option. The tabulated value of chi-square at 8 degrees of freedom and 5 percent is about 15.5, and the computed value of 8.0 is below it, so the hypothesis of no association is not rejected. The other options of 6, 4 and 3 do not match the number of rows and columns of the table.
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