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**statmajor** Let the result of a random experiment be classified as one of the mutually exclusive and exhaustive ways A1, A2, A3 and also one of the mutually exclusive and exhaustive ways B1, B2, B3, B4. 200 independent trials of the experiment result in the following data:

B1 B2 B3 B4

A1 10 21 15 6

A2 11 27 21 13

A3 6 19 27 24

Test at 0.05 significance level the hypothesis of independence. Null hypothesis $\displaystyle H_0 : P(A_i \cap B_j) = P(A_i)P(B_j)$ against the alternate hypothesis (dependence exists)

Would the test statistic be:

$\displaystyle Q(X) = \Sigma \Sigma \frac{(X_{ij} - \frac{C_j R_i}{n})^2}{\frac{C_j R_i}{n}}$

where Cj = the sum of column j, and Ri = sum of row i

so for $\displaystyle X_{11} = \frac{(10 - \frac{(27)(52)}{200})^2}{\frac{(27)(52)}{200}}$

and so forth?