Step 1: Confirm Statement I by recalling what a hygrometer does.
A hygrometer is an instrument built to sense atmospheric moisture directly, using elements such as human hair or electronic capacitive sensors whose physical properties change with humidity, so it gives a direct reading of relative humidity. This matches Statement I, making it correct.
Step 2: Confirm Statement II by recalling the psychrometer method.
The dry and wet bulb thermometer arrangement, known as a psychrometer, is the most widely used field and laboratory method because it only needs two ordinary thermometers, one kept wet by a wick, and the difference between the two readings is looked up on a psychrometric chart or table to get relative humidity. Its simplicity and low cost make it the most common method in practice, so Statement II is also correct.
Step 3: Note that the two methods are complementary rather than contradictory.
One describes a direct sensing instrument and the other an indirect, calculation based method, and both coexist as valid, standard techniques rather than one disproving the other.
\[ \boxed{Both Statement (I) and Statement (II) are correct.} \]