Best Dx Lens Does The F/ Stop Speed Of A Non DX Lens Change On A DX Sensor?

Does the f/ stop speed of a non DX lens change on a DX sensor? - best dx lens

I will buy af/1.8 Nikon 50mm lens for my D200. I know that complies with the DX sensor one 75mm lens, but still act like 1.8 or the difference in the formats will also have an impact?