Statement II:
In aniline, the lone pair of electrons on the nitrogen atom is
delocalised into the benzene ring through resonance.
As a result, the availability of the lone pair for protonation decreases.
Hence, aniline is a weak base.
Therefore, Statement II is true.
Statement I:
In acetamide ($CH_3CONH_2$), the lone pair on nitrogen is involved in
strong resonance with the adjacent carbonyl group.
The resonance structure places negative charge on the oxygen atom,
which is highly electronegative, making the lone pair on nitrogen
much less available for protonation.
Thus, acetamide is far less basic than aniline.
Numerically,
\[
\text{p}K_b(\text{aniline}) \approx 9.4,\qquad
\text{p}K_b(\text{acetamide}) \approx 14.5
\]
Since higher p$K_b$ implies weaker basicity, acetamide is weaker than aniline.
Hence, the statement “aniline is less basic than acetamide” is false.
Conclusion:
\[
\boxed{\text{Statement I is false but Statement II is true}}
\]
\[
\boxed{\text{Option (D)}}
\]