Step 1: Treat the bottle as a lens.
A thin-walled glass sphere full of liquid behaves like a fat lens. Its bending power comes only from the liquid inside, since the glass wall is negligibly thin.
Step 2: Remember the key idea about lenses.
The more the refractive index of the lens material differs from the surrounding air, the more strongly it bends light, so the more power it has and the shorter its focal length.
Step 3: Write the dependence in words.
Power grows with the factor $(n - 1)$, where $n$ is the liquid's index and air has index $1$. A bigger $(n - 1)$ means a stronger lens.
Step 4: Swap in the new liquid.
The new liquid has a higher refractive index than water, so its $(n - 1)$ is larger.
Step 5: Translate to focal length.
A larger $(n - 1)$ means more power, and more power means a smaller focal length, because focal length is the reciprocal of power.
Step 6: State the comparison.
Therefore the new focal length is shorter than before. \[ \boxed{f' \lt f} \]