`i have a sealed cylinder sitting in my lab that contains 1,000.0 ml of gas. if i compress the cylinder and change the volume to 500.0 ml, keeping the temperature constant, what will i expect to see happen to the pressure?

Because the temperature remains constant, we can apply Boyle's Law which states that 
pV = constant
where
p = pressure
V = volume

Define the two states of the gas.

State 1
Pressure = p₁
Volume = 1000 ml

State 2
Pressure = p₂
Volume = 500 ml

Apply Boyle's law.
1000p₁ = 500p₂
2 = p₂/p₁

By halving the volume, the pressure doubles.

The pressure increases by a factor of 2.

Amethod of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.