Transistor Resistor Math Question

I have a PNP resistor. The supply voltage is 3V and the current draw out the other end is 160mA. I am trying to determine the resistor value between the digital pin and the base. The micro controller is running at 3V. Does anyone know the exact resistance and watts that the resistor should be able to dissipate? Hopefully I have provided enough information, but please let me know if I have not.

If you could explain how you get the answer that would be greatly appreciated so that I will know how to in the future. Thanks in advance for your help.

The base resistor is just to limit the current drawn from the Arduino pin. The minimum current will depend on the 'current gain' or 'beta' of the transistor. If the gain is 100 and you want 160 mA out you only need 1.6 mA in. A 1k resistor should limit the current to about 3 mA which should be plenty.

Does anyone know the exact resistance and watts that the resistor should be able to dissipate?

As johnwasser said the exact value does not matter, so long as it supplies two to ten times the minimum current.
As to the wattage dissipation of the resistor, you can not get a resistor with a power rating small enough for this to be a problem.
Power is I squared R, with R being 1K and I being 3.3mA then the power is 0.01089 W, so just over one hundredth of a watt, any resistor you buy is at least 10 times greater than this, and the most popular quarter watt is 25 times more than you need.

Thank you!