Fuel Pump Issues?

I am looking for some input on what I think is a fuel related problem before I tear into my car.

Engine is a 383 with a mechanical Carter fuel pump.

The pump is about 8-10 yrs old and does not leak.

Problem is the engine is stumbling at low RPM's like its running out of gas.

If I pump the gas pedal many times is sputters and starts idling normally. When I am driving under normal conditions it seems to be OK.

At low RPM when you give it gas it will backfire through the carb as well.

I noticed bubbles in the clear fuel filter and it seems like the filter is not filling up all the way. I am suspecting a bad fuel pump but do not have a pressure gauge to determine if this is the case.

Am I on the right track (Bad Fuel Pump) or do I need to spend the $$ to buy a pressure gauge to test the theory first.

I have a lot of experience with electric pumps but not much with mechanical pumps so I am not sure what to look for besides what I have mentioned above.

Help appreciated.

Thanks,

Mop