Step 1: Analyze n-hexane + n-heptane.
Both are nonpolar with similar intermolecular forces, forming an ideal solution. Option 1 is correct.
Step 2: Analyze C$_2$H$_5$OH + H$_2$O.
Hydrogen bonding in pure components is stronger than in the mixture, leading to positive deviation. Option 2 is correct.
Step 3: Analyze CHCl$_3$ + CH$_3$COCH$_3$.
Hydrogen bonding forms between CHCl$_3$ and CH$_3$COCH$_3$, stronger than in pure components, leading to negative deviation. Option 3 is correct.
Step 4: Analyze C$_2$H$_5$OH + CH$_3$COCH$_3$.
Hydrogen bonding in pure ethanol is stronger than the interactions in the mixture with acetone, leading to positive deviation, not an ideal solution. Option 4 is incorrect.
Thus, the statement that is not correct is $ \boxed{C_2H_5OH + CH_3COCH_3 - Ideal solution} $.