Step 1: Understanding the Concept
Short day plants (SDP) such as Xanthium and soybean flower only when the night is longer than a critical length.
What matters is the length of the continuous dark period, not the day.
Step 2: Check Statement (I)
SDP need a long, uninterrupted dark period for flowering, so Statement (I) is correct.
Step 3: Check Statement (II)
A short flash of light in the middle of the dark period breaks the night, so the critical dark length is lost and the SDP does not flower.
Statement (II) says the opposite, so it is incorrect.
Step 4: Conclusion
Statement (I) is correct and Statement (II) is incorrect.
Final Answer:
Statement (I) is correct but Statement (II) is incorrect.
\[ \boxed{\text{(C) }\text{Statement (I) is correct but Statement (II) is incorrect.}} \]