Dominant contribution of v = 0 → v = 1 transition in vibrational spectroscopy
The reference should really be to the Boltzmann distribution where the  population is proportional to $\exp(-E_n/(k_\mathrm BT))$  where $E_n$ is the energy of the $n^{th}$ energy level. This shows that the population is greatest when $n$ is small. Also you need to know that absorption is proportional to the population difference between any two levels. As the vibrational frequency is generally a few hundred wavenumbers, or higher, and $k_\mathrm BT$ at room temperature $\approx 210$ wavenumbers you can see that the population of $n= 0$ levels can be very large compared to that when $n\gt 0$.