I am doing an acoustics experiment in physics. I tested how the amplitude of sound was affected based on the temperature of the air. I know that the speed of sound is affected by temperature. Sound will travel faster in colder air. Likewise it travels fastest in solids, followed by liquids then gases. I wanted to test a correlation with loudness. However, I found that in colder temperatures the decibel reading was actually lower. Is this correct? If sound travels best in colder air, shouldn't the reading be higher?

Yes, your results are most likely accurate. Even though the speed of sound is faster at cooler temperatures, this has no bearing on the amplitude since the velocity of a wave depends only on the frequency and wavelength. In a longitudinal wave the displacements of the particles are parallel to the direction of travel of the wave. So the amplitude is the maximum displacement of a particle in the medium from its equilibrium position. In cooler temperatures, where the particles are really close to each other, this means that there displacements will tend to be shorter in length, corresponding to a smaller amplitude. This is also why sound travels faster at cooler temperatures, the particels transferring the energy don't have as far to go. This also makes sense just by thinking about hearing sounds through walls which can be thought of as molecules in a cooler state, even though they are at room temperature. It is harder to hear sounds through walls than it is to hear it in air. Let me know if this helped you or not.