- Statement I is true. The \( \text{OCH}_3 \) group has a \( +R \) effect (electron-donating resonance effect), which stabilizes the carbocation formed during the reaction.
- Statement II is false. The \( \text{NO}_2 \) group has a \( -R \) effect (electron-withdrawing resonance effect), which destabilizes the carbanion, not stabilizes it.
Thus, the correct answer is that Statement I is true, and Statement II is false.
Final Answer: (C) Statement I is true but Statement II is false.