Step 1: Understanding the Concept:
Boiling points of organic compounds are determined by the strength of intermolecular forces: Hydrogen bonding > Dipole-dipole interaction > Van der Waals forces.
Step 2: Detailed Explanation:
Analysis of Statement I: Aldehydes and ketones contain a polar carbonyl group ($C=O$). This leads to dipole-dipole interactions between molecules. Hydrocarbons only have weak dispersion forces. Thus, carbonyl compounds have higher boiling points than hydrocarbons of similar mass. Statement I is **Correct**.
Analysis of Statement II: Alcohols have a hydrogen atom bonded to oxygen ($-OH$), enabling strong intermolecular hydrogen bonding. Aldehydes and ketones do not have $H$ bonded to $O$, so they cannot form intermolecular hydrogen bonds with themselves. Therefore, alcohols have much higher boiling points. Statement II is **Correct**.
Step 3: Final Answer:
Both statements correctly describe the trends in boiling points based on intermolecular forces.