A sample of 60 binary pairs gives counts n₁₁=10,n₁₀=20,n₀₁=20,n₀₀=10. Test independence of X,Y by Pearson’s chi-square test. Which statement gives the null distribution and observed statistic?
Correct answer: (A) Central χ² with 1 degree of freedom;20/3.
Explanation
Both margins are (30,30),so every expected cell count is 15. Pearson statistic=4·(5²/15)=20/3. Independence in a 2×2 table gives (2−1)(2−1)=1 degree of freedom. **A**. The χ² null distribution is the usual large-sample approximation,not an exact finite discrete law.
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